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×#33610 |
| 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)(28,43)(29,41)(30,34)(31,38)(33,36)(37,48)(39,54)(40,50)(42,47)(44,55)(45,52)(46,53)(49,51);(24,26,36,51,29,39,44,53,30,40,42,52,27,37,28,38)(25,31,43,48,32,45,47,50,34,46,55,54,41,49,33,35);(21,23)(24,25)(26,31)(27,41)(28,33)(29,32)(30,34)(35,38)(36,43)(37,49)(39,45)(40,46)(42,55)(44,47)(48,51)(50,53)(52,54);(24,27,30,29)(25,32,34,41)(26,37,40,39)(28,42,44,36)(31,45,46,49)(33,43,47,55)(35,48,50,54)(38,52,53,51)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26598);