Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33764 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33770 |
| 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 | |
576 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,26)(23,25)(24,27)(28,29,32,38)(30,41,43,35)(31,40,34,37)(33,48,47,51)(36,54,55,44)(39,46,57,50)(42,52,45,56)(49,58,59,53);(20,22)(21,24)(23,27)(25,26)(28,30,32,43)(29,35,38,41)(31,45,34,42)(33,44,47,54)(36,48,55,51)(37,56,40,52)(39,53,57,58)(46,59,50,49);(22,27)(24,26)(28,30)(29,36)(31,42)(32,43)(33,49)(34,45)(35,51)(37,53)(38,55)(39,56)(40,58)(41,48)(44,50)(46,54)(47,59)(52,57);(21,25)(24,26)(28,31,32,34)(29,37,38,40)(30,42,43,45)(33,46,47,50)(35,52,41,56)(36,53,55,58)(39,51,57,48)(44,49,54,59)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26758);