Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33495 |
| 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 | |
564 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)(28,29,32,37,33,38,44,52,31,36,42,50,43,51,55,59)(30,35,40,48,41,49,54,58,39,34,45,46,53,47,56,57);(20,22)(21,24)(23,27)(25,26)(28,30)(29,34)(31,39)(32,40)(33,41)(35,36)(37,46)(38,47)(42,45)(43,53)(44,54)(48,50)(49,51)(52,57)(55,56)(58,59);(22,27)(24,26)(28,30)(29,35)(31,39)(32,40)(33,41)(34,36)(37,48)(38,49)(42,45)(43,53)(44,54)(46,50)(47,51)(52,58)(55,56)(57,59);(21,25)(24,26)(29,36)(30,39)(37,50)(38,51)(40,45)(41,53)(52,59)(54,56)1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26483);