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×#33705 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C23×C19 | C2×D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
578 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)(28,29,35,41)(30,37,42,54)(31,36,45,51)(32,39,48,57)(33,38,49,56)(34,50,47,40)(43,55,58,53)(44,59,46,52);(21,24)(25,27)(28,30,33,43,34,44,48,45,35,42,49,58,47,46,32,31)(29,36,39,52,40,53,56,54,41,51,57,59,50,55,38,37);(20,22,23,26)(21,25,24,27)(28,31,32,46,47,58,49,42,35,45,48,44,34,43,33,30)(29,37,38,55,50,59,57,51,41,54,56,53,40,52,39,36);(30,42)(31,45)(36,51)(37,54)(43,58)(44,46)(52,59)(53,55)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26693);