Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18446 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18452 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1028 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)(21,26)(22,30)(23,34)(27,40)(28,38)(29,35)(31,33)(32,47)(36,49)(39,44)(41,51)(42,48)(43,50)(45,46);(20,21,24,29)(22,27,31,41)(23,35,34,26)(25,28,37,43)(30,44,33,42)(32,48,46,39)(36,50,49,38)(40,45,51,47);(22,31)(23,36)(26,38)(27,41)(30,33)(32,45)(34,49)(35,50)(39,40)(42,44)(46,47)(48,51);(20,22,24,31)(21,27,29,41)(23,32,34,46)(25,33,37,30)(26,39,35,48)(28,42,43,44)(36,47,49,45)(38,51,50,40)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11440);