Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C89 · Schur multiplier (H2) = C24 |
| direct product | C89×#24925 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C89 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C89 |
| prime radical | C89×#3012 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C89 ◁ C22×C4×C89 ◁ G | |
904 conjugacy classes of subgroups.
| minimal degree | μ(G) = 113 |
| transitive degree | μt(G) = 5696 |
A minimal faithful permutation representation — 4 generators on 113 points:
(1,2)(3,5)(4,6)(7,8)(9,10)(11,19)(12,16)(13,20)(14,17)(15,18)(21,23)(22,24)(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);(1,3,4,7)(2,5,6,8)(9,11)(10,12)(13,21)(14,16)(15,22)(17,24)(18,23)(19,20);(2,6)(5,8)(9,12)(10,16)(11,20)(13,19)(14,24)(15,23)(17,22)(18,21);(9,12)(10,11)(13,24)(14,19)(15,23)(16,20)(17,21)(18,22)3827 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 17913);