Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#23520 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C22×C19 | C2×#121 |
| prime radical | C22×C19×#135 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C23×C4×C19 ◁ G | |
1350 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
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)(26,35)(27,39)(28,33)(29,44)(30,34)(31,37)(32,43)(36,52)(38,47)(40,51)(41,54)(42,50)(45,48)(46,55)(49,53);(24,26)(25,31)(27,40)(28,37)(29,45)(30,38)(32,49)(33,47)(34,48)(35,44)(36,43)(39,46)(41,55)(42,53)(50,51)(52,54);(21,23)(24,27,29,42,30,43,28,41)(25,32,33,50,34,39,44,54)(26,36,37,53,38,40,45,55)(31,46,35,51,48,49,47,52);(24,28,30,29)(25,33,34,44)(26,37,38,45)(27,41,43,42)(31,47,48,35)(32,50,39,54)(36,53,40,55)(46,52,49,51)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16508);