Finite Group DatabasebetaFinite Group Databasebeta| order | 21376 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C167 · Schur multiplier (H2) = C24 |
| direct product | #2395×C167 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C167 | C23 |
| commutator, Frattini, cosocle | C23 | C24×C167 |
| socle | C23×C167 | C24 |
| prime radical | C22×D4×C167 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C167 ◁ G | |
560 conjugacy classes of subgroups.
| minimal degree | μ(G) = 187 |
| transitive degree | μt(G) = 10688 |
A minimal faithful permutation representation — 4 generators on 187 points:
(5,6)(7,10)(8,9)(11,12)(13,14)(15,17)(16,18)(19,20)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187);(1,2)(3,4)(6,9)(10,12)(13,15,16,19)(14,17,18,20);(2,4)(14,18)(17,20);(5,7,8,11)(6,10,9,12)7348 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21376, 1127);