List of abstract groups of order 64

Group GAP4(64,1) [C64]
Group GAP4(64,2) [C8 x C8]
Group GAP4(64,3) [C8 : C8]
Group GAP4(64,4) [((C8 x C2) : C2) : C2]
Group GAP4(64,5) [(C4 x C2) : C8]
Group GAP4(64,6) [(C8 x C4) : C2]
Group GAP4(64,7) [Q8 : C8]
Group GAP4(64,8) [((C8 x C2) : C2) : C2]
Group GAP4(64,9) [(C2 x Q8) : C4]
Group GAP4(64,10) [(C8 : C4) : C2]
Group GAP4(64,11) [(C2 x C2) . ((C4 x C2) : C2) = (C4 x C2) . (C4 x C2)]
Group GAP4(64,12) [(C4 : C8) : C2]
Group GAP4(64,13) [(C2 x C2) . ((C4 x C2) : C2) = (C4 x C2) . (C4 x C2)]
Group GAP4(64,14) [(C2 x C2) . ((C4 x C2) : C2) = (C4 x C2) . (C4 x C2)]
Group GAP4(64,15) [C8 : C8]
Group GAP4(64,16) [C8 : C8]
Group GAP4(64,17) [(C8 x C2) : C4]
Group GAP4(64,18) [(C8 x C2) : C4]
Group GAP4(64,19) [C4 . (C4 x C4)]
Group GAP4(64,20) [(C4 x C4) : C4]
Group GAP4(64,21) [(C8 x C2) : C4]
Group GAP4(64,22) [(C4 x C2) . D8 = C4 . (C4 x C4)]
Group GAP4(64,23) [(C4 x C2 x C2) : C4]
Group GAP4(64,24) [(C8 : C2) : C4]
Group GAP4(64,25) [(C8 x C2) : C4]
Group GAP4(64,26) [C16 x C4]
Group GAP4(64,27) [C16 : C4]
Group GAP4(64,28) [C16 : C4]
Group GAP4(64,29) [(C16 x C2) : C2]
Group GAP4(64,30) [(C16 : C2) : C2]
Group GAP4(64,31) [(C16 x C2) : C2]
Group GAP4(64,32) [((C8 : C2) : C2) : C2]
Group GAP4(64,33) [(C4 x C2 x C2) : C4]
Group GAP4(64,34) [(((C4 x C2) : C2) : C2) : C2]
Group GAP4(64,35) [(C4 x C4) : C4]
Group GAP4(64,36) [(C2 . ((C4 x C2) : C2) = (C2 x C2) . (C4 x C2)) : C2]
Group GAP4(64,37) [C2 . (((C4 x C2) : C2) : C2) = (C4 x C2) . (C4 x C2)]
Group GAP4(64,38) [(C16 x C2) : C2]
Group GAP4(64,39) [Q16 : C4]
Group GAP4(64,40) [(C16 x C2) : C2]
Group GAP4(64,41) [(C16 : C2) : C2]
Group GAP4(64,42) [(C16 : C2) : C2]
Group GAP4(64,43) [C2 . ((C8 x C2) : C2) = C8 . (C4 x C2)]
Group GAP4(64,44) [C4 : C16]
Group GAP4(64,45) [C8 . D8 = C4 . (C8 x C2)]
Group GAP4(64,46) [C16 : C4]
Group GAP4(64,47) [C16 : C4]
Group GAP4(64,48) [C16 : C4]
Group GAP4(64,49) [C4 . D16 = C8 . (C4 x C2)]
Group GAP4(64,50) [C32 x C2]
Group GAP4(64,51) [C32 : C2]
Group GAP4(64,52) [D64]
Group GAP4(64,53) [QD64]
Group GAP4(64,54) [Q64]
Group GAP4(64,55) [C4 x C4 x C4]
Group GAP4(64,56) [C2 x ((C4 x C2) : C4)]
Group GAP4(64,57) [(C4 x C4) : C4]
Group GAP4(64,58) [C4 x ((C4 x C2) : C2)]
Group GAP4(64,59) [C4 x (C4 : C4)]
Group GAP4(64,60) [(C2 x ((C4 x C2) : C2)) : C2]
Group GAP4(64,61) [(C2 x (C4 : C4)) : C2]
Group GAP4(64,62) [((C4 x C2) : C4) : C2]
Group GAP4(64,63) [(C4 x C4) : C4]
Group GAP4(64,64) [(C4 x C4) : C4]
Group GAP4(64,65) [(C4 x C4) : C4]
Group GAP4(64,66) [(C2 x (C4 : C4)) : C2]
Group GAP4(64,67) [(C4 x C2 x C2 x C2) : C2]
Group GAP4(64,68) [(C4 : C4) : C4]
Group GAP4(64,69) [(C4 x C4 x C2) : C2]
Group GAP4(64,70) [(C4 : C4) : C4]
Group GAP4(64,71) [(C4 x C4 x C2) : C2]
Group GAP4(64,72) [(C2 x Q8) : C4]
Group GAP4(64,73) [(C2 x C2 x D8) : C2]
Group GAP4(64,74) [(C2 x C2 x Q8) : C2]
Group GAP4(64,75) [(C2 x ((C4 x C2) : C2)) : C2]
Group GAP4(64,76) [(C4 x C2) : Q8]
Group GAP4(64,77) [(C2 x (C4 : C4)) : C2]
Group GAP4(64,78) [(C2 x (C4 : C4)) : C2]
Group GAP4(64,79) [(C2 x C2 x C2) . (C2 x C2 x C2)]
Group GAP4(64,80) [(C2 x (C4 : C4)) : C2]
Group GAP4(64,81) [(C2 x C2 x C2) . (C2 x C2 x C2)]
Group GAP4(64,82) [(C2 x C2 x C2) . (C2 x C2 x C2)]
Group GAP4(64,83) [C8 x C4 x C2]
Group GAP4(64,84) [C2 x (C8 : C4)]
Group GAP4(64,85) [C4 x (C8 : C2)]
Group GAP4(64,86) [(C8 x C4) : C2]
Group GAP4(64,87) [C2 x ((C8 x C2) : C2)]
Group GAP4(64,88) [(C2 x (C8 : C2)) : C2]
Group GAP4(64,89) [(C8 x C2 x C2) : C2]
Group GAP4(64,90) [C2 x (((C4 x C2) : C2) : C2)]
Group GAP4(64,91) [(((C4 x C2) : C2) : C2) : C2]
Group GAP4(64,92) [C2 x ((C8 : C2) : C2)]
Group GAP4(64,93) [C2 x (C2 . ((C4 x C2) : C2) = (C2 x C2) . (C4 x C2))]
Group GAP4(64,94) [(C2 x (C8 : C2)) : C2]
Group GAP4(64,95) [C2 x ((C8 x C2) : C2)]
Group GAP4(64,96) [C2 x (Q8 : C4)]
Group GAP4(64,97) [(C8 x C2 x C2) : C2]
Group GAP4(64,98) [(C2 x (C8 : C2)) : C2]
Group GAP4(64,99) [(C2 x (C8 : C2)) : C2]
Group GAP4(64,100) [(Q8 : C4) : C2]
Group GAP4(64,101) [C2 x ((C4 x C4) : C2)]
Group GAP4(64,102) [(C2 x (C8 : C2)) : C2]
Group GAP4(64,103) [C2 x (C4 : C8)]
Group GAP4(64,104) [(C4 : C8) : C2]
Group GAP4(64,105) [(C4 : C8) : C2]
Group GAP4(64,106) [C2 x (C8 : C4)]
Group GAP4(64,107) [C2 x (C8 : C4)]
Group GAP4(64,108) [(C8 : C4) : C2]
Group GAP4(64,109) [(C8 : C4) : C2]
Group GAP4(64,110) [C2 x (C4 . D8 = C4 . (C4 x C2))]
Group GAP4(64,111) [(C4 . D8 = C4 . (C4 x C2)) : C2]
Group GAP4(64,112) [(C8 x C4) : C2]
Group GAP4(64,113) [(C4 : C8) : C2]
Group GAP4(64,114) [(C8 x C4) : C2]
Group GAP4(64,115) [C8 x D8]
Group GAP4(64,116) [(C8 x C2 x C2) : C2]
Group GAP4(64,117) [(C8 x C4) : C2]
Group GAP4(64,118) [C4 x D16]
Group GAP4(64,119) [C4 x QD16]
Group GAP4(64,120) [C4 x Q16]
Group GAP4(64,121) [(C4 x Q8) : C2]
Group GAP4(64,122) [Q16 : C4]
Group GAP4(64,123) [(C4 x D8) : C2]
Group GAP4(64,124) [(C8 x C4) : C2]
Group GAP4(64,125) [((C4 x C4) : C2) : C2]
Group GAP4(64,126) [C8 x Q8]
Group GAP4(64,127) [C8 : Q8]
Group GAP4(64,128) [(C2 x C2 x D8) : C2]
Group GAP4(64,129) [(C2 x C2 x Q8) : C2]
Group GAP4(64,130) [(C2 x D16) : C2]
Group GAP4(64,131) [(C2 x QD16) : C2]
Group GAP4(64,132) [(C2 x Q16) : C2]
Group GAP4(64,133) [(C2 x Q16) : C2]
Group GAP4(64,134) [((C4 x C4) : C2) : C2]
Group GAP4(64,135) [((C4 x C4) : C2) : C2]
Group GAP4(64,136) [((C4 x C4) : C2) : C2]
Group GAP4(64,137) [((C4 x C4) : C2) : C2]
Group GAP4(64,138) [(((C4 x C2) : C2) : C2) : C2]
Group GAP4(64,139) [(((C4 x C2) : C2) : C2) : C2]
Group GAP4(64,140) [(C4 x D8) : C2]
Group GAP4(64,141) [(C2 x QD16) : C2]
Group GAP4(64,142) [(Q8 : C4) : C2]
Group GAP4(64,143) [C4 : Q16]
Group GAP4(64,144) [(C4 x D8) : C2]
Group GAP4(64,145) [(C2 x Q16) : C2]
Group GAP4(64,146) [(C8 x C2 x C2) : C2]
Group GAP4(64,147) [(C8 x C2 x C2) : C2]
Group GAP4(64,148) [(C2 x Q16) : C2]
Group GAP4(64,149) [(C2 x (C8 : C2)) : C2]
Group GAP4(64,150) [(C2 x (C8 : C2)) : C2]
Group GAP4(64,151) [(C2 x Q16) : C2]
Group GAP4(64,152) [(C2 x QD16) : C2]
Group GAP4(64,153) [(C2 x D16) : C2]
Group GAP4(64,154) [(C2 x Q16) : C2]
Group GAP4(64,155) [(C8 : C4) : C2]
Group GAP4(64,156) [Q8 : Q8]
Group GAP4(64,157) [(C8 : C4) : C2]
Group GAP4(64,158) [Q8 : Q8]
Group GAP4(64,159) [(C8 : C4) : C2]
Group GAP4(64,160) [(C2 x C2) . (C2 x D8) = (C4 x C2) . (C2 x C2 x C2)]
Group GAP4(64,161) [(C2 x (C4 : C4)) : C2]
Group GAP4(64,162) [(C2 x (C4 : C4)) : C2]
Group GAP4(64,163) [((C8 x C2) : C2) : C2]
Group GAP4(64,164) [(Q8 : C4) : C2]
Group GAP4(64,165) [(Q8 : C4) : C2]
Group GAP4(64,166) [(C8 : C4) : C2]
Group GAP4(64,167) [(C8 x C4) : C2]
Group GAP4(64,168) [(C2 x C2) . (C2 x D8) = (C4 x C2) . (C2 x C2 x C2)]
Group GAP4(64,169) [(C8 x C4) : C2]
Group GAP4(64,170) [(Q8 : C4) : C2]
Group GAP4(64,171) [((C8 x C2) : C2) : C2]
Group GAP4(64,172) [(C2 x C2) . (C2 x D8) = (C4 x C2) . (C2 x C2 x C2)]
Group GAP4(64,173) [(C8 x C4) : C2]
Group GAP4(64,174) [(C8 x C4) : C2]
Group GAP4(64,175) [C4 : Q16]
Group GAP4(64,176) [(C8 x C4) : C2]
Group GAP4(64,177) [(C2 x D16) : C2]
Group GAP4(64,178) [(C2 x Q16) : C2]
Group GAP4(64,179) [C8 : Q8]
Group GAP4(64,180) [(C2 x C2) . (C2 x D8) = (C4 x C2) . (C2 x C2 x C2)]
Group GAP4(64,181) [C8 : Q8]
Group GAP4(64,182) [C8 : Q8]
Group GAP4(64,183) [C16 x C2 x C2]
Group GAP4(64,184) [C2 x (C16 : C2)]
Group GAP4(64,185) [(C16 x C2) : C2]
Group GAP4(64,186) [C2 x D32]
Group GAP4(64,187) [C2 x QD32]
Group GAP4(64,188) [C2 x Q32]
Group GAP4(64,189) [(C16 x C2) : C2]
Group GAP4(64,190) [(C2 x D16) : C2]
Group GAP4(64,191) [(C2 x Q16) : C2]
Group GAP4(64,192) [C4 x C4 x C2 x C2]
Group GAP4(64,193) [C2 x C2 x ((C4 x C2) : C2)]
Group GAP4(64,194) [C2 x C2 x (C4 : C4)]
Group GAP4(64,195) [C2 x ((C4 x C4) : C2)]
Group GAP4(64,196) [C2 x C4 x D8]
Group GAP4(64,197) [C2 x C4 x Q8]
Group GAP4(64,198) [C4 x ((C4 x C2) : C2)]
Group GAP4(64,199) [(C4 x D8) : C2]
Group GAP4(64,200) [(C4 x Q8) : C2]
Group GAP4(64,201) [(C4 x Q8) : C2]
Group GAP4(64,202) [C2 x ((C2 x C2 x C2 x C2) : C2)]
Group GAP4(64,203) [C2 x ((C4 x C2 x C2) : C2)]
Group GAP4(64,204) [C2 x ((C2 x Q8) : C2)]
Group GAP4(64,205) [C2 x ((C4 x C2 x C2) : C2)]
Group GAP4(64,206) [(C4 x C2 x C2 x C2) : C2]
Group GAP4(64,207) [C2 x ((C4 x C4) : C2)]
Group GAP4(64,208) [C2 x ((C2 x C2) . (C2 x C2 x C2))]
Group GAP4(64,209) [C2 x ((C4 x C4) : C2)]
Group GAP4(64,210) [(C4 x C4 x C2) : C2]
Group GAP4(64,211) [C2 x ((C4 x C4) : C2)]
Group GAP4(64,212) [C2 x (C4 : Q8)]
Group GAP4(64,213) [(C4 x C4 x C2) : C2]
Group GAP4(64,214) [(C4 x Q8) : C2]
Group GAP4(64,215) [(C2 x C2 x D8) : C2]
Group GAP4(64,216) [(C2 x C2 x D8) : C2]
Group GAP4(64,217) [(C2 x C2 x Q8) : C2]
Group GAP4(64,218) [(C2 x ((C4 x C2) : C2)) : C2]
Group GAP4(64,219) [(C4 x D8) : C2]
Group GAP4(64,220) [(C4 x D8) : C2]
Group GAP4(64,221) [(C4 x D8) : C2]
Group GAP4(64,222) [(C4 x Q8) : C2]
Group GAP4(64,223) [(C4 x Q8) : C2]
Group GAP4(64,224) [((C2 x Q8) : C2) : C2]
Group GAP4(64,225) [(C4 : Q8) : C2]
Group GAP4(64,226) [D8 x D8]
Group GAP4(64,227) [(C2 x C2 x D8) : C2]
Group GAP4(64,228) [(C4 x D8) : C2]
Group GAP4(64,229) [(C2 x C2 x Q8) : C2]
Group GAP4(64,230) [Q8 x D8]
Group GAP4(64,231) [(C4 x D8) : C2]
Group GAP4(64,232) [(C4 x D8) : C2]
Group GAP4(64,233) [(C4 x Q8) : C2]
Group GAP4(64,234) [(C4 x D8) : C2]
Group GAP4(64,235) [(C4 x Q8) : C2]
Group GAP4(64,236) [(C4 x D8) : C2]
Group GAP4(64,237) [(C4 x Q8) : C2]
Group GAP4(64,238) [Q8 : Q8]
Group GAP4(64,239) [Q8 x Q8]
Group GAP4(64,240) [(C4 x D8) : C2]
Group GAP4(64,241) [((C4 x C2 x C2) : C2) : C2]
Group GAP4(64,242) [((C4 x C4) : C2) : C2]
Group GAP4(64,243) [((C2 x C2) . (C2 x C2 x C2)) : C2]
Group GAP4(64,244) [((C4 x C4) : C2) : C2]
Group GAP4(64,245) [(C2 x C2) . (C2 x C2 x C2 x C2)]
Group GAP4(64,246) [C8 x C2 x C2 x C2]
Group GAP4(64,247) [C2 x C2 x (C8 : C2)]
Group GAP4(64,248) [C2 x ((C8 x C2) : C2)]
Group GAP4(64,249) [(C2 x (C8 : C2)) : C2]
Group GAP4(64,250) [C2 x C2 x D16]
Group GAP4(64,251) [C2 x C2 x QD16]
Group GAP4(64,252) [C2 x C2 x Q16]
Group GAP4(64,253) [C2 x ((C8 x C2) : C2)]
Group GAP4(64,254) [C2 x ((C2 x D8) : C2)]
Group GAP4(64,255) [C2 x ((C2 x Q8) : C2)]
Group GAP4(64,256) [(C2 x (C8 : C2)) : C2]
Group GAP4(64,257) [(C2 x D16) : C2]
Group GAP4(64,258) [(C2 x QD16) : C2]
Group GAP4(64,259) [(C2 x Q16) : C2]
Group GAP4(64,260) [C4 x C2 x C2 x C2 x C2]
Group GAP4(64,261) [C2 x C2 x C2 x D8]
Group GAP4(64,262) [C2 x C2 x C2 x Q8]
Group GAP4(64,263) [C2 x C2 x ((C4 x C2) : C2)]
Group GAP4(64,264) [C2 x ((C2 x D8) : C2)]
Group GAP4(64,265) [C2 x ((C2 x Q8) : C2)]
Group GAP4(64,266) [(C2 x ((C4 x C2) : C2)) : C2]
Group GAP4(64,267) [C2 x C2 x C2 x C2 x C2 x C2]

Database of Galois polynomials by Bill Allombert and Igor Schein.
Last Modified: Thu, 19 Dec 2013 12:12:28 +0100
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