Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18446 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#18464 |
| 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 ◁ C2×C42×C19 ◁ G | |
970 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)(23,35)(27,40)(28,38)(29,36)(31,34)(33,48)(37,47)(39,44)(41,51)(42,50)(43,49)(45,46);(20,21,24,29)(22,27,31,41)(23,36,35,26)(25,28,32,42)(30,44,34,43)(33,49,46,39)(37,50,47,38)(40,45,51,48);(22,31)(23,37)(26,38)(27,41)(30,34)(33,45)(35,47)(36,50)(39,40)(43,44)(46,48)(49,51);(20,22,32,30)(21,27,42,44)(23,33,47,45)(24,31,25,34)(26,39,50,40)(28,43,29,41)(35,46,37,48)(36,49,38,51)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11452);