Finite Group DatabasebetaFinite Group Databasebeta| order | 20096 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2069 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C157 · Schur multiplier (H2) = C22 |
| direct product | #2070×C157 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C157 | #396 |
| commutator, Frattini, cosocle | C22×C4 | C23×C157 |
| prime radical | C23×C157 | C2×Q8 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C157 ◁ C22×C4×C157 ◁ G | |
196 conjugacy classes of subgroups.
| minimal degree | μ(G) = 189 |
| transitive degree | μt(G) = 5024 |
A minimal faithful permutation representation — 3 generators on 189 points:
(1,2,7,10,6,11,5,19)(3,12,21,23,15,28,14,8)(4,9,20,24,18,25,17,26)(13,27,30,22,16,31,29,32)(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);(1,3,5,14,6,15,7,21)(2,8,10,12,11,23,19,28)(4,16,17,30,18,13,20,29)(9,22,24,31,25,32,26,27);(1,4,6,18)(2,9,11,25)(3,13,15,16)(5,20,7,17)(8,22,23,32)(10,26,19,24)(12,27,28,31)(14,30,21,29)3611 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20096, 802);