Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33522 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#33585 |
| 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 ◁ C19×#117 ◁ C19×#405 ◁ G | |
748 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
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)(21,23)(24,25)(26,30)(27,31)(28,41)(29,34)(32,38)(33,39)(35,43)(36,42)(37,51)(40,47)(44,50)(45,49)(46,52)(48,53)(54,55);(20,21,22,23)(24,26)(25,30)(27,36)(28,37)(29,35)(31,42)(32,44)(33,45)(34,43)(38,50)(39,49)(40,48)(41,51)(46,54)(47,53)(52,55);(25,31)(27,38)(28,39)(30,42)(32,33)(34,47)(36,50)(37,49)(40,52)(41,46)(43,53)(44,45)(48,55)(51,54);(26,35)(30,43)(36,48)(37,49)(42,53)(44,54)(45,51)(50,55)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26573);