Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#11345 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #120 |
| commutator | C24 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C22×C19 | #385 |
| prime radical | C24×C19 | C22×C4 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C23×C4×C19 ◁ G | |
698 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,23)(24,25,28,33,29,32,40,46)(26,30,36,42,35,43,48,53)(27,31,39,45,38,44,51,54)(34,41,47,52,37,49,50,55);(24,26)(25,30)(27,37,38,34)(28,36)(29,35)(31,41,44,49)(32,43)(33,42)(39,50,51,47)(40,48)(45,52,54,55)(46,53);(20,21,22,23)(24,27)(25,31)(26,34)(28,39)(29,38)(30,41)(32,44)(33,45)(35,37)(36,47)(40,51)(42,52)(43,49)(46,54)(48,50)(53,55)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4333);