Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11704 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C2×C4 |
| direct product | C19×#11750 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#102 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C19×#466 | C22 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
326 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)(21,25,26,27)(28,29,32,37,34,39,33,38)(30,40,43,53,41,56,44,57)(31,45,47,36,49,54,48,55)(35,46,51,42,50,59,52,58);(20,21)(22,25)(23,27)(24,26)(28,30)(29,35)(31,46)(32,44)(33,43)(34,41)(36,53)(37,52)(38,51)(39,50)(40,54)(42,48)(45,56)(47,58)(49,59)(55,57);(20,22,24,23)(21,25,26,27)(30,41)(35,50)(40,56)(42,58)(43,44)(46,59)(51,52)(53,57)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4738);