Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#22322 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C19 | C24 |
| commutator | C23 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C23×C19 | C23×C4 |
| prime radical | C24×C19 | C22×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C19 ◁ G | |
652 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 51 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)(30,33)(31,32)(34,35)(36,37,40,44,41,38,42,46)(39,43,48,50,47,45,49,51);(20,22)(21,24)(23,27)(25,26)(36,38,40,46,41,37,42,44)(39,43,48,50,47,45,49,51);(22,27)(24,26)(29,32)(33,35)(36,39)(37,43)(38,45)(40,48)(41,47)(42,49)(44,50)(46,51);(21,25)(24,26)(28,30,31,34)(29,33,32,35)(39,47)(43,45)(48,49)(50,51)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 15310);