Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11855 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C2×C4 |
| direct product | C19×#11963 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#102 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C4×C8 | C23×C19 |
| prime radical | C19×#3147 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
396 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 3 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,25,23,24,26,27)(28,29,33,38,31,40,47,37,34,39,50,55,48,36,32,49)(30,41,44,53,46,54,59,57,45,56,58,35,42,52,43,51);(21,24)(22,26)(28,30)(29,35)(31,42)(32,44)(33,43)(34,45)(36,51)(37,54)(38,56)(39,53)(40,57)(41,55)(46,48)(47,58)(49,52)(50,59);(21,24)(25,27)(28,31,34,48)(29,36,39,40)(30,42,45,46)(32,33,47,50)(35,51,53,57)(37,38,49,55)(41,54,56,52)(43,58,59,44)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4951);