Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33481 |
| 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×#121 | C8 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C19 ◁ G | |
508 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)(28,29,31,36,32,37,41,49,33,35,42,47,43,48,53,57)(30,34,39,45,40,46,52,56,38,44,50,54,51,55,58,59);(21,24)(25,27)(30,38)(34,44)(39,50)(40,51)(45,54)(46,55)(52,58)(56,59);(28,30,31,39,32,40,41,52,33,38,42,50,43,51,53,58)(29,34,36,45,37,46,49,56,35,44,47,54,48,55,57,59);(20,22,23,26)(21,25,24,27)(29,35)(34,44)(36,47)(37,48)(45,54)(46,55)(49,57)(56,59)1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26469);