Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#11285 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #124 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C22×C19 | #394 |
| prime radical | C24×C19 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C23×C4×C19 ◁ G | |
606 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)(20,21,22,23)(24,25)(26,30,35,42)(27,31,38,45)(28,33)(29,32)(34,41)(36,43,49,54)(37,44)(39,46,51,52)(40,47)(48,53)(50,55);(24,26)(25,30,32,42)(27,37,38,50)(28,36)(29,35)(31,44)(33,43,47,54)(34,39,48,51)(40,49)(41,52)(45,55)(46,53);(24,27)(25,31,32,45)(26,34,35,48)(28,39)(29,38)(30,41)(33,46,47,52)(36,37,49,50)(40,51)(42,53)(43,44)(54,55)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4273);