Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33605 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#33719 |
| 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×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
834 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)(26,34)(27,39)(28,31)(29,42)(30,37)(32,35)(33,40)(36,46)(38,53)(41,54)(43,51)(44,55)(45,50)(47,49)(48,52);(24,26,35,49,29,38,41,51,28,36,50,55,40,52,27,37)(25,30,39,48,33,44,45,46,31,43,54,53,42,47,32,34);(20,21,22,23)(25,31)(30,43)(32,45)(33,42)(34,46)(39,54)(44,47)(48,53);(26,36)(30,43)(34,46)(37,51)(38,52)(44,47)(48,53)(49,55)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26707);