Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C89 · Schur multiplier (H2) = C25 |
| direct product | C89×#24323 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C89 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C89 |
| prime radical | C2×#41×C89 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C89 ◁ C2×C42×C89 ◁ G | |
1004 conjugacy classes of subgroups.
| minimal degree | μ(G) = 113 |
| transitive degree | μt(G) = 5696 |
A minimal faithful permutation representation — 4 generators on 113 points:
(1,2,5,8)(3,7,4,6)(9,10)(11,14)(12,20)(13,19)(15,17)(16,24)(18,22)(21,23)(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);(1,3,5,4)(2,6,8,7)(9,11,14,10)(12,21,23,20)(13,19,15,17)(16,22,18,24);(9,12,14,23)(10,16,11,18)(13,22,15,24)(17,21,19,20);(1,4,5,3)(2,7,8,6)(9,13,14,15)(10,17,11,19)(12,22,23,24)(16,21,18,20)3827 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 17311);