Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#32748 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C24×C19 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C22×C42×C19 ◁ G | |
658 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)(22,24)(23,25)(26,27)(28,29,31,34)(30,33,35,32)(36,37,40,43)(38,41,45,49)(39,42,46,50)(44,48,47,51);(20,22)(21,24)(23,26)(25,27)(28,30,31,35)(29,32,34,33)(38,44)(39,46)(41,48)(42,50)(45,47)(49,51);(21,25)(24,27)(28,30)(29,33)(31,35)(32,34)(36,38,40,45)(37,41,43,49)(39,47,46,44)(42,51,50,48);(22,26)(24,27)(30,35)(32,33)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 25736);