Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13323 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#13323 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #1999 |
| commutator, Frattini, cosocle | C22×C8 | C23×C19 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ C2×C19×#131 ◁ G | |
534 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)(21,27)(22,32)(23,36)(24,25)(28,45)(29,43)(30,37)(31,44)(33,46)(34,38)(35,41)(39,40)(42,47)(48,51);(20,21)(22,33)(23,37)(24,29)(25,30)(26,31)(27,36)(28,32)(34,42)(35,47)(38,46)(39,44)(40,43)(41,48)(45,49)(50,51);(20,22)(21,28)(23,38)(24,41)(25,32)(26,35)(27,42)(29,33)(30,47)(31,48)(34,40)(36,50)(37,51)(39,49)(43,45)(44,46)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6311);