Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#13024 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #447 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| socle | C2×C19 | #1879 |
| prime radical | C19×#3414 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C22×C4×C19 ◁ C2×C19×#97 ◁ G | |
466 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)(20,21,26,32,27,33,25,44,28,34,45,51,43,50,24,31)(22,35,36,48,37,49,23,39,38,30,41,29,40,46,42,47);(20,22,27,40,28,38,43,37)(21,29,33,39,34,48,50,47)(23,25,36,45,42,24,41,26)(30,31,49,32,35,44,46,51);(20,23)(21,30)(22,25)(24,38)(26,37)(27,36)(28,42)(29,31)(32,39)(33,49)(34,35)(40,45)(41,43)(44,48)(46,50)(47,51)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6012);