Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13374 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#13374 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2023 |
| commutator, Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C2×C19×#135 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ C19×#405 ◁ G | |
360 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,30,32,47)(23,35)(24,39)(25,28)(26,33,31,49)(27,37)(29,41)(34,43,40,48)(36,45,51,42)(38,46)(44,50);(20,21)(22,31,32,26)(23,27)(24,29)(25,28)(30,33,47,49)(34,45,40,42)(35,37)(36,48,51,43)(38,44)(39,41)(46,50);(20,22)(21,26)(23,36)(24,40)(25,32)(27,43)(28,31)(29,45)(30,46)(33,50)(34,41)(35,47)(37,49)(38,51)(39,42)(44,48)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6362);