# Group GAP4(96,31)

Name: C3 : (C2 . ((C4 x C2) : C2) = (C2 x C2) . (C4 x C2))
Maximal quotients:GAP4(32,8) GAP4(48,14)
Real polynomial:
```x^96-2880*x^94+3602880*x^92-2645798400*x^90+1293871947840*x^88-4519683743616\
00*x^86+117924890394585600*x^84-23700847418545766400*x^82+375231694846288060\
8000*x^80-475905259631483564544000*x^78+48984783544266049175040000*x^76-4133\
722625759790969163776000*x^74+288315150702075246595806720000*x^72-1672775972\
3380942614277877760000*x^70+811492832842202516700688404480000*x^68-330503085\
96714736439422869504000000*x^66+1133663761156224934945733730647040000*x^64-3\
2827877140657839442903534252032000000*x^62+803854297293177440683475984240640\
000000*x^60-16662263367763927359491060806955827200000*x^58+29247991404917958\
9334944025917124608000000*x^56-4347048852409107285686936277960523776000000*x\
^54+54665467604805563747305374869019131904000000*x^52-5808814913151979018573\
40415353602179072000000*x^50+5205954251732073538824838578258207424512000000*\
x^48-39252687447787316290713918128491419402240000000*x^46+248216821253530441\
454886878037960091238400000000*x^44-1311347470327862203671978605358729155051\
520000000*x^42+5761381390965440592791290580974874107576320000000*x^40-209355\
11018338503395960103892712070316032000000000*x^38+62517034896133171871952358\
653468864990412800000000*x^36-1522701169848778567194087259289292814417920000\
00000*x^34+299887938109728379357096096609133388005376000000000*x^32-47282387\
7485232877199854783562302057611264000000000*x^30+590110323349668581192829194\
362253677166592000000000*x^28-5757471055917830872040257310203524730060800000\
00000*x^26+433283221838444513791926548804672491094016000000000*x^24-24806388\
2046094803687164791664244613447680000000000*x^22+106593662196531579079650236\
282557421322240000000000*x^20-3394194709502412940449547324813712818176000000\
0000*x^18+7912551647445507850583258298739285032960000000000*x^16-13331070591\
53776624567509699059829964800000000000*x^14+15973378174793071780475000479285\
2480000000000000*x^12-13312221185714727071075770925737574400000000000*x^10+7\
47255439120177113951555343613952000000000000*x^8-269505667865747278046441515\
25376000000000000*x^6+581874934555561044601447907328000000000000*x^4-6692424\
442727272325364842496000000000000*x^2+30983446494107742247059456000000000000```
Common denominator of the automorphisms:
```2527736452641525082677588762334625838177994269871909820520201711751958080581\
9694803553641326667006236246896018369056620549920174686291992255089688365636\
0570105279983885334321650452724237657263451650712470244682174888211217503945\
1998527157501668649441484263912428181255312062400156251366453527055951804829\
6244710889570244176270943208204934037107696992256000000000000```
Complex polynomial:
```x^96+2880*x^94+3602880*x^92+2645798400*x^90+1293871947840*x^88+4519683743616\
00*x^86+117924890394585600*x^84+23700847418545766400*x^82+375231694846288060\
8000*x^80+475905259631483564544000*x^78+48984783544266049175040000*x^76+4133\
722625759790969163776000*x^74+288315150702075246595806720000*x^72+1672775972\
3380942614277877760000*x^70+811492832842202516700688404480000*x^68+330503085\
96714736439422869504000000*x^66+1133663761156224934945733730647040000*x^64+3\
2827877140657839442903534252032000000*x^62+803854297293177440683475984240640\
000000*x^60+16662263367763927359491060806955827200000*x^58+29247991404917958\
9334944025917124608000000*x^56+4347048852409107285686936277960523776000000*x\
^54+54665467604805563747305374869019131904000000*x^52+5808814913151979018573\
40415353602179072000000*x^50+5205954251732073538824838578258207424512000000*\
x^48+39252687447787316290713918128491419402240000000*x^46+248216821253530441\
454886878037960091238400000000*x^44+1311347470327862203671978605358729155051\
520000000*x^42+5761381390965440592791290580974874107576320000000*x^40+209355\
11018338503395960103892712070316032000000000*x^38+62517034896133171871952358\
653468864990412800000000*x^36+1522701169848778567194087259289292814417920000\
00000*x^34+299887938109728379357096096609133388005376000000000*x^32+47282387\
7485232877199854783562302057611264000000000*x^30+590110323349668581192829194\
362253677166592000000000*x^28+5757471055917830872040257310203524730060800000\
00000*x^26+433283221838444513791926548804672491094016000000000*x^24+24806388\
2046094803687164791664244613447680000000000*x^22+106593662196531579079650236\
282557421322240000000000*x^20+3394194709502412940449547324813712818176000000\
0000*x^18+7912551647445507850583258298739285032960000000000*x^16+13331070591\
53776624567509699059829964800000000000*x^14+15973378174793071780475000479285\
2480000000000000*x^12+13312221185714727071075770925737574400000000000*x^10+7\
47255439120177113951555343613952000000000000*x^8+269505667865747278046441515\
25376000000000000*x^6+581874934555561044601447907328000000000000*x^4+6692424\
442727272325364842496000000000000*x^2+30983446494107742247059456000000000000```
Common denominator of the automorphisms:
```2527736452641525082677588762334625838177994269871909820520201711751958080581\
9694803553641326667006236246896018369056620549920174686291992255089688365636\
0570105279983885334321650452724237657263451650712470244682174888211217503945\
1998527157501668649441484263912428181255312062400156251366453527055951804829\
6244710889570244176270943208204934037107696992256000000000000```

Database of Galois polynomials by Bill Allombert and Igor Schein.