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×#33612 |
| 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 | |
694 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)(20,21)(22,23)(25,30)(27,31)(28,38)(32,40)(33,41)(34,48)(36,44)(37,50)(39,45)(42,43)(46,55)(47,53)(49,54)(51,52);(24,25,31,43,28,34,39,41,29,33,45,48,38,42,27,30)(26,32,44,52,37,46,49,53,35,47,54,55,50,51,36,40);(21,23)(24,26)(25,32)(27,36)(28,37)(29,35)(30,40)(31,44)(33,47)(34,46)(38,50)(39,49)(41,53)(42,51)(43,52)(45,54)(48,55);(25,33)(26,35)(30,41)(34,42)(36,49)(37,50)(43,48)(44,54)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26600);