Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C89 · Schur multiplier (H2) = C24 |
| direct product | C89×#26995 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C89 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C89 |
| prime radical | #537×C89 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C89 ◁ C22×C4×C89 ◁ G | |
762 conjugacy classes of subgroups.
| minimal degree | μ(G) = 129 |
| transitive degree | μt(G) = 5696 |
A minimal faithful permutation representation — 4 generators on 129 points:
(1,2)(3,7)(4,6)(5,8)(9,10)(11,17)(12,25)(13,28)(14,21)(15,20)(16,23)(18,29)(19,26)(22,37)(24,32)(27,31)(30,36)(33,38)(34,39)(35,40)(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);(1,3,4,8)(2,5,6,7)(9,11,14,23,15,12,26,24)(10,16,19,17,20,32,21,25)(13,22,29,38,30,27,40,39)(18,31,28,33,35,37,36,34);(2,6)(5,7)(9,12)(10,17)(11,15)(13,22)(14,24)(16,21)(18,34)(19,32)(20,25)(23,26)(27,30)(28,31)(29,38)(33,35)(36,37)(39,40);(2,6)(5,7)(9,13,14,29,15,30,26,40)(10,18,19,28,20,35,21,36)(11,22,23,38,12,27,24,39)(16,31,17,33,32,37,25,34)3560 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 19983);