Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23872 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#23873 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2403 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
1686 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)(22,30)(23,34)(24,37)(25,29)(26,32)(27,35)(28,39)(31,42)(33,44)(36,45)(38,41)(40,43)(46,47)(48,50)(49,51);(20,22,25,33)(21,26,29,41)(23,31,36,48)(24,38,39,32)(27,42,43,50)(28,44,37,30)(34,46,45,51)(35,49,40,47);(24,39)(26,41)(28,37)(32,38)(34,45)(35,40)(42,50)(47,49);(20,23)(21,27)(22,31)(24,40)(25,36)(26,42)(28,45)(29,43)(30,46)(32,49)(33,48)(34,37)(35,39)(38,47)(41,50)(44,51)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16861);