Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C89 · Schur multiplier (H2) = C28 |
| direct product | C89×#61627 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C89 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C89 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C89 ◁ #525×C89 ◁ G | |
2050 conjugacy classes of subgroups.
| minimal degree | μ(G) = 129 |
| transitive degree | μt(G) = 5696 |
A minimal faithful permutation representation — 5 generators on 129 points:
(1,2)(3,7)(4,6)(5,8)(9,10)(11,16)(12,24)(13,18)(14,27)(15,19)(17,25)(20,35)(21,30)(22,31)(23,32)(26,33)(28,34)(29,36)(37,40)(38,39)(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);(1,3)(2,5)(4,8)(6,7)(9,11)(10,16)(12,20)(13,21)(14,22)(15,23)(17,29)(18,30)(19,32)(24,35)(25,36)(26,38)(27,31)(28,37)(33,39)(34,40);(9,12,15,26)(10,17,19,34)(11,20,23,38)(13,25,14,28)(16,29,32,40)(18,33,27,24)(21,36,22,37)(30,39,31,35);(3,8)(5,7)(9,13,15,14)(10,18,19,27)(11,21,23,22)(12,25,26,28)(16,30,32,31)(17,33,34,24)(20,36,38,37)(29,39,40,35);(2,6)(5,7)(9,13,15,14)(10,18,19,27)(11,22,23,21)(12,25,26,28)(16,31,32,30)(17,33,34,24)(20,37,38,36)(29,35,40,39)4361 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 54615);