Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#33594 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #459 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| socle | C2×C19 | C2×#459 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C22×C4×C19 ◁ C2×C4×C8×C19 ◁ G | |
696 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 4 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)(22,31)(23,36)(24,30)(25,40)(26,41)(27,32)(28,34)(29,33)(35,48)(37,51)(38,47)(39,43)(42,44)(45,49)(46,50);(20,22,25,34,27,35,24,26)(21,28,30,31,32,41,40,48)(23,33,38,49,39,50,37,42)(29,43,44,47,46,36,45,51);(20,23)(21,29)(22,33)(24,37)(25,38)(26,42)(27,39)(28,43)(30,44)(31,47)(32,46)(34,49)(35,50)(36,41)(40,45)(48,51);(20,24,27,25)(21,30,32,40)(22,26,35,34)(23,37,39,38)(28,31,41,48)(29,44,46,45)(33,42,50,49)(36,51,43,47)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26582);