Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33830 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33876 |
| 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 ◁ C4×D4×C19 ◁ C8×D4×C19 ◁ G | |
564 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)(20,21,23,25)(22,26,27,24)(28,29)(30,39)(31,36)(32,44)(33,48)(34,38)(35,42)(37,46)(40,55)(41,57)(43,54)(45,51)(47,56)(49,53)(50,58)(52,59);(20,22)(21,24)(23,27)(25,26)(30,40)(35,50)(39,55)(41,49)(42,58)(45,59)(51,52)(53,57);(28,30,34,40)(29,35,38,50)(31,41,33,49)(32,45,47,59)(36,51,48,52)(37,53,54,57)(39,56,55,44)(42,43,58,46);(22,27)(24,26)(28,31,34,33)(29,36,38,48)(30,41,40,49)(32,43,47,46)(35,51,50,52)(37,44,54,56)(39,57,55,53)(42,45,58,59)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26864);