Finite Group DatabasebetaFinite Group Databasebeta| order | 20096 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C157 · Schur multiplier (H2) = C25 |
| direct product | #2935×C157 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C157 | C24 |
| commutator | C22 | C23×C4×C157 |
| Frattini, cosocle | C2×C4 | C24×C157 |
| socle | C22×C157 | C23×C4 |
| prime radical | #532×C157 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C157 ◁ G | |
492 conjugacy classes of subgroups.
| minimal degree | μ(G) = 177 |
| transitive degree | μt(G) = 10048 |
A minimal faithful permutation representation — 4 generators on 177 points:
(1,2)(3,4)(5,6,9,13,10,7,11,15)(8,12,17,19,16,14,18,20)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177);(2,4)(8,16)(12,14)(17,18)(19,20);(5,7,9,15,10,6,11,13)(8,12,17,19,16,14,18,20);(5,8)(6,12)(7,14)(9,17)(10,16)(11,18)(13,19)(15,20)7850 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20096, 1667);