Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17405 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#21883 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C24×C19 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C19×#117 ◁ G | |
954 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)(21,24)(22,26)(28,29,33,37,32,36,46,53)(30,38,41,55,40,34,48,50)(31,42,45,54,44,35,47,52)(39,49,56,58,43,51,57,59);(20,21)(22,25)(23,24)(26,27)(28,30)(29,34)(31,43)(32,40)(33,41)(35,51)(36,38)(37,50)(39,44)(42,49)(45,57)(46,48)(47,56)(52,59)(53,55)(54,58);(21,24)(25,27)(28,31,32,44)(29,35,36,42)(30,39,40,43)(33,47,46,45)(34,49,38,51)(37,54,53,52)(41,57,48,56)(50,59,55,58);(20,22,23,26)(21,25,24,27)(29,36)(30,40)(35,42)(37,53)(39,43)(41,48)(52,54)(56,57)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14871);