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×#33881 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C19×#3280 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C4×D4×C19 ◁ C8×D4×C19 ◁ G | |
570 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1216 |
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)(28,29,33,38)(30,34,39,49)(31,35,44,52)(32,45,43,37)(36,53,51,42)(40,50,54,46)(41,58,55,48)(47,56,59,57);(20,22)(21,24)(23,27)(25,26)(28,30)(29,34)(31,40)(32,41)(33,39)(35,50)(36,47)(37,48)(38,49)(42,57)(43,55)(44,54)(45,58)(46,52)(51,59)(53,56);(29,35)(30,39)(31,42)(32,43)(34,46)(36,37)(38,52)(40,56)(44,53)(45,51)(47,58)(48,59)(49,50)(54,57);(22,27)(24,26)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26869);