Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C89 · Schur multiplier (H2) = C24 |
| direct product | C89×#26855 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C89 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C89 |
| prime radical | C89×#2002 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C89 ◁ C22×C4×C89 ◁ G | |
764 conjugacy classes of subgroups.
| minimal degree | μ(G) = 113 |
| transitive degree | μt(G) = 2848 |
A minimal faithful permutation representation — 4 generators on 113 points:
(1,2)(3,8)(4,6)(5,7)(9,10)(11,12)(13,19)(14,18)(15,20)(16,17)(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);(1,3,5,4)(2,6,7,8)(9,10,14,19,15,20,13,18)(11,12,17,23,22,24,21,16);(1,4,5,3)(2,6,7,8)(9,11,13,21,15,22,14,17)(10,16,18,24,20,23,19,12);(2,7)(6,8)(9,12,13,16,15,24,14,23)(10,17,18,11,20,21,19,22)3560 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 19843);