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) = C2×C4 |
| direct product | C19×#13288 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#102 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C23×C19 | C2×D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
354 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1216 |
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)(22,26)(23,24)(25,27)(28,29)(30,40,45,55)(31,46)(32,36)(33,50)(34,39)(35,43,53,48)(37,41)(38,47)(42,52,57,59)(44,51,58,56)(49,54);(21,24)(25,26)(28,30,41,57,47,58,32,48,34,45,31,42,33,44,49,43)(29,35,36,51,50,59,37,55,39,53,54,56,38,52,46,40);(20,22,23,27)(21,25,24,26)(28,31,47,49,34,41,33,32)(29,36,50,37,39,54,38,46)(30,42,58,43,45,57,44,48)(35,51,59,55,53,56,52,40)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6276);