Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33607 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23×C4 |
| direct product | C19×#33703 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C2×C19×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C19×#117 ◁ C19×#405 ◁ G | |
570 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)(28,29,35,40)(30,41,43,42)(31,47,37,33)(32,48,50,38)(34,51,49,39)(36,52,53,44)(45,55,58,56)(46,54,59,57);(21,24)(25,27)(28,30,33,45,34,46,32,44,35,43,47,58,49,59,50,52)(29,36,38,54,39,55,37,41,40,53,48,57,51,56,31,42);(20,22,23,26)(21,25,24,27)(28,31,32,39,49,48,33,29,35,37,50,51,34,38,47,40)(30,42,44,55,59,57,45,36,43,41,52,56,46,54,58,53);(30,43)(36,53)(41,42)(44,52)(45,58)(46,59)(54,57)(55,56)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26691);