Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11677 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#11682 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#102 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C4×C8 | C23×C19 |
| prime radical | C19×#466 | C4 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
322 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)(20,21,23,26,24,22,27,25)(28,29)(30,39,42,55)(31,35)(32,46)(33,38)(34,41,50,59)(36,44)(37,45)(40,53,43,56)(47,49,57,51)(48,52)(54,58);(20,22)(21,24)(23,25)(26,27)(28,30)(29,34)(31,43)(32,47)(33,42)(35,51)(36,53)(37,49)(38,50)(39,52)(40,45)(41,58)(44,59)(46,55)(48,57)(54,56);(21,22)(25,26)(28,31,33,45)(29,35,38,37)(30,40,42,43)(32,44,48,58)(34,49,50,51)(36,52,54,46)(39,53,55,56)(41,57,59,47)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4670);