Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33607 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#33611 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×#41×C19 ◁ C2×C19×#131 ◁ G | |
674 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 2432 |
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)(27,32)(28,42)(29,41)(30,34)(31,38)(33,43)(36,48)(37,49)(39,55)(40,51)(44,45)(46,52)(47,54)(50,53);(24,26,36,52,29,39,28,38,30,40,43,53,27,37,44,54)(25,31,45,55,32,46,33,35,34,47,42,49,41,50,48,51);(21,23)(24,25)(26,31)(27,41)(28,33)(29,32)(30,34)(35,38)(36,45)(37,50)(39,46)(40,47)(42,43)(44,48)(49,53)(51,54)(52,55);(24,27,30,29)(25,32,34,41)(26,37,40,39)(28,36,44,43)(31,46,47,50)(33,42,48,45)(35,49,51,55)(38,52,54,53)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26599);