Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C89 · Schur multiplier (H2) = C26 |
| direct product | C89×#24297 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C89 | #2408 |
| commutator, Frattini, cosocle | C22×C4 | C24×C89 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C89 ◁ C22×C4×C89 ◁ G | |
1334 conjugacy classes of subgroups.
| minimal degree | μ(G) = 121 |
| transitive degree | μt(G) = 2848 |
A minimal faithful permutation representation — 4 generators on 121 points:
(1,2,8,11)(3,6,14,7)(4,15,19,12)(5,13,22,27)(9,17,24,18)(10,21,25,20)(16,23,31,32)(26,29,28,30)(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);(1,3,6,11,8,14,7,2)(4,9,17,12,19,24,18,15)(5,13,20,25,22,27,21,10)(16,23,29,26,31,32,30,28);(1,4)(2,9)(3,12)(5,16)(6,17)(7,18)(8,19)(10,23)(11,24)(13,26)(14,15)(20,29)(21,30)(22,31)(25,32)(27,28);(1,5,7,21,8,22,6,20)(2,10,14,27,11,25,3,13)(4,16,18,30,19,31,17,29)(9,23,15,28,24,32,12,26)3560 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 17285);