Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33605 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23×C4 |
| direct product | C19×#33708 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C19×#3147 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
590 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)(22,25)(23,24)(26,27)(28,29)(30,43)(31,36)(32,38)(33,52)(34,54)(35,42)(37,48)(39,44)(40,53)(41,51)(45,59)(46,55)(47,56)(49,58)(50,57);(21,24)(25,27)(28,30,44,49,32,47,53,50,35,48,34,46,51,45,33,31)(29,36,52,59,41,55,54,37,42,57,40,56,38,58,39,43);(20,22,23,26)(21,25,24,27)(28,31,33,45,51,46,34,48,35,50,53,47,32,49,44,30)(29,37,39,55,38,59,40,36,42,43,54,58,41,56,52,57);(28,32,35,51)(29,38,42,41)(30,45,48,47)(31,46,50,49)(33,44,53,34)(36,55,57,58)(37,56,43,59)(39,40,54,52)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26696);