Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33764 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33808 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C23×C19 | C2×D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C19×#117 ◁ C19×#405 ◁ G | |
442 conjugacy classes of subgroups.
| minimal degree | μ(G) = 67 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 67 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,28)(23,26)(24,27)(25,30)(29,34)(31,33)(32,35)(36,37,41,46)(38,42,47,55)(39,43,52,59)(40,53,51,45)(44,60,58,50)(48,54,61,65)(49,64,62,57)(56,67,66,63);(20,22,24,30)(21,25,27,28)(23,31,32,29)(26,34,35,33)(36,38)(37,42)(39,48)(40,49)(41,47)(43,54)(44,56)(45,57)(46,55)(50,63)(51,62)(52,61)(53,64)(58,66)(59,65)(60,67);(20,23,24,32)(21,26,27,35)(22,29,30,31)(25,33,28,34)(37,43)(39,50)(40,51)(42,54)(44,45)(46,59)(48,63)(49,62)(52,60)(53,58)(55,65)(56,57)(61,67)(64,66);(21,27)(25,28)(26,35)(33,34)(38,47)(42,55)(48,61)(49,62)(54,65)(56,66)(57,64)(63,67)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26796);