Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#22294 |
| 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 | |
702 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)(31,35)(32,34)(36,37,41,38,40,43,48,45)(39,42,47,44,46,49,51,50);(20,22)(21,24)(23,27)(25,26)(28,30,32,31)(29,33,34,35)(36,38,41,43,40,45,48,37)(39,44,47,49,46,50,51,42);(22,27)(24,26)(28,31,32,30)(29,33,34,35)(36,39)(37,42)(38,44)(40,46)(41,47)(43,49)(45,50)(48,51);(21,25)(24,26)(37,43)(38,45)(39,46)(47,51)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 15282);