Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C22×C4 |
| direct product | C19×#32841 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C22×D4×C19 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C43×C19 ◁ G | |
632 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)(20,21,23,25)(22,24,26,27)(29,33)(34,35)(36,37)(38,42)(39,43)(40,41)(44,50)(45,48)(46,49)(47,51);(20,22)(21,24)(23,26)(25,27)(29,34)(30,32)(33,35)(37,41)(39,46)(42,48)(44,47);(21,25)(24,27)(28,29)(30,34)(31,33)(32,35)(36,38,40,45)(37,42,41,48)(39,47,46,44)(43,51,49,50);(22,26)(24,27)(28,30,31,32)(29,34,33,35)(36,39,40,46)(37,43,41,49)(38,44,45,47)(42,50,48,51)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 25829);