Finite Group DatabasebetaFinite Group Databasebeta| order | 22599 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9×C31 · Schur multiplier (H2) = C3 |
| direct product | C31×#10624727 |
| subgroup | G/H | |
|---|---|---|
| center | C3×C9×C31 | C33 |
| commutator | C32 | C32×C9×C31 |
| Frattini, cosocle | C3×C9 | C33×C31 |
| socle | C32×C31 | C32×C9 |
| prime radical | C33×C31 | C3×C9 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C3×C9×C31 ◁ G | |
196 conjugacy classes of subgroups.
| minimal degree | μ(G) = 67 |
| transitive degree | μt(G) = 7533 |
A minimal faithful permutation representation — 3 generators on 67 points:
(2,4,7)(5,9,8)(10,11,17,15,21,31,25,18,32,16,13,19,29,28,34,24,26,30,14,20,27,23,35,36,12,22,33)(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);(1,2,5,3,4,8,6,7,9)(10,12,23,14,24,29,16,25,15)(11,18,28,20,22,21,13,26,35)(17,30,31,27,32,36,19,33,34);(10,13,27,15,28,36,25,26,33,16,20,17,29,35,31,24,22,32,14,11,19,23,21,34,12,18,30)4743 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22599, 287);