Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C89 · Schur multiplier (H2) = C23 |
| direct product | C89×#23372 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C89 | C24 |
| commutator | C23 | C23×C4×C89 |
| Frattini, cosocle | C22×C4 | C24×C89 |
| socle, prime radical | C23×C89 | C23×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C89 ◁ G | |
584 conjugacy classes of subgroups.
| minimal degree | μ(G) = 113 |
| transitive degree | μt(G) = 22784 |
A minimal faithful permutation representation — 4 generators on 113 points:
(2,5)(3,7)(9,10)(11,14)(12,16)(13,15)(17,18,21,24,20,22,19,23)(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);(1,2)(3,8)(4,5)(6,7)(9,11,14,10)(12,16,13,15)(18,22)(23,24);(2,5)(6,8)(9,12,14,13)(10,15,11,16);(1,3,4,7)(2,6,5,8)(9,13,14,12)(10,15,11,16)(17,19,20,21)(18,23,22,24)4628 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 16360);