Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#21843 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C22×D4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C24×C19 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C19×#117 ◁ G | |
970 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,23)(24,25)(26,32)(27,30)(28,31)(29,34)(33,38)(35,37)(36,39)(40,41)(42,45)(43,46)(44,48)(47,51)(49,53)(50,52)(54,55);(24,26,28,34)(25,29,31,32)(27,35,36,33)(30,38,39,37)(40,42)(41,45)(43,50)(44,49)(46,52)(47,54)(48,53)(51,55);(24,27,28,36)(25,30,31,39)(26,33,34,35)(29,37,32,38)(41,46)(43,51)(45,52)(47,48)(50,55)(53,54);(25,31)(29,32)(30,39)(37,38)(42,49)(45,53)(50,55)(52,54)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14831);