Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C22×C4 |
| direct product | C19×#21436 |
| 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 | |
688 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)(22,25)(23,24)(26,27)(28,29)(30,33)(31,32)(34,35)(36,37,41,38,40,43,48,45)(39,42,47,44,46,49,51,50);(21,24)(25,27)(36,38,41,43,40,45,48,37)(39,44,47,49,46,50,51,42);(20,22,23,26)(21,25,24,27)(29,32)(33,35)(36,39,40,46)(37,42,43,49)(38,44,45,50)(41,47,48,51);(28,30,31,34)(29,33,32,35)(39,46)(42,49)(44,50)(47,51)1444 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14424);