Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#34644 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C19 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C19 |
| socle | C23×C19 | C25 |
| prime radical | C24×C19 | C24 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C19 ◁ G | |
1570 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 5 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)(28,29,31,33)(30,34,35,32)(36,37)(38,41)(39,43)(40,42)(44,47)(45,48)(46,49)(50,51);(21,24)(25,27)(36,38)(37,41)(39,45)(40,44)(42,47)(43,48)(46,50)(49,51);(28,30,31,35)(29,32,33,34)(38,44)(41,47)(45,50)(48,51);(20,22,23,26)(21,25,24,27)(37,42)(41,47)(43,49)(48,51);(36,39,40,46)(37,43,42,49)(38,45,44,50)(41,48,47,51)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 27632);