Finite Group DatabasebetaFinite Group Databasebeta| order | 20096 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1655 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C157 · Schur multiplier (H2) = C22 |
| direct product | #1658×C157 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C157 | #120 |
| commutator, Frattini, cosocle | C42 | C23×C157 |
| prime radical | #127×C157 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C157 ◁ C42×C157 ◁ G | |
182 conjugacy classes of subgroups.
| minimal degree | μ(G) = 189 |
| transitive degree | μt(G) = 10048 |
A minimal faithful permutation representation — 3 generators on 189 points:
(2,6)(4,11)(7,15)(8,12)(9,13)(14,16)(19,25)(20,27)(22,30)(23,28)(26,29)(31,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189);(1,2,5,8)(3,7,10,16)(4,12,11,6)(9,14,13,15)(17,18,21,24)(19,22,26,31)(20,28,27,23)(25,32,29,30);(1,3,5,10)(2,7,8,16)(4,13,11,9)(6,14,12,15)(17,19)(18,22)(20,29)(21,26)(23,32)(24,31)(25,27)(28,30)3140 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20096, 390);