Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33494 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C19 | C24 |
| commutator | C22 | C23×C8×C19 |
| Frattini, cosocle | C2×C8 | C24×C19 |
| socle | C22×C19 | C23×C8 |
| prime radical | C19×#532 | C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C19 ◁ G | |
556 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)(22,26)(23,25)(24,27)(28,29,31,36,32,37,42,50,33,38,43,51,44,52,55,59)(30,34,40,45,41,46,54,56,39,35,47,48,53,49,57,58);(20,22)(21,24)(23,27)(25,26)(28,30)(29,34)(31,40)(32,41)(33,39)(35,38)(36,45)(37,46)(42,54)(43,47)(44,53)(48,51)(49,52)(50,56)(55,57)(58,59);(22,27)(24,26)(28,30)(29,35)(31,40)(32,41)(33,39)(34,38)(36,48)(37,49)(42,54)(43,47)(44,53)(45,51)(46,52)(50,58)(55,57)(56,59);(21,25)(24,26)(30,39)(34,35)(40,47)(41,53)(45,48)(46,49)(54,57)(56,58)1444 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26482);