Finite Group DatabasebetaFinite Group Databasebeta| order | 20096 |
| nilpotency class | 6 |
| isoclinism | isoclinic class of D64 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C157 · Schur multiplier (H2) = C2 |
| direct product | D64×C157 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C157 | D32 |
| commutator, Frattini, cosocle | C32 | C22×C157 |
| LCS | G ▷ C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C157 ◁ C4×C157 ◁ C8×C157 ◁ C16×C157 ◁ C32×C157 ◁ G | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 221 |
| transitive degree | μt(G) = 10048 |
A minimal faithful permutation representation — 2 generators on 221 points:
(1,2)(3,8)(4,19)(5,23)(6,26)(7,13)(9,14)(10,15)(11,20)(12,24)(16,36)(17,38)(18,30)(21,54)(22,52)(25,56)(27,40)(28,39)(29,47)(31,46)(32,49)(33,42)(34,55)(35,45)(37,53)(41,57)(43,51)(44,50)(48,61)(58,64)(59,63)(60,62)(65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221);(2,8)(3,14)(4,15)(5,20)(6,24)(9,10)(11,36)(12,38)(13,30)(16,46)(17,49)(18,42)(19,27)(21,55)(22,45)(23,28)(25,53)(26,29)(31,51)(32,50)(33,35)(34,57)(37,61)(39,40)(41,47)(43,44)(48,64)(52,59)(54,58)(56,60)(62,63)5495 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20096, 161);