Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#36679 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C19 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C19 |
| socle | C23×C19 | C25 |
| prime radical | C22×D4×C19 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C19 ◁ G | |
1506 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)(30,32)(31,33)(34,35)(36,37,40,43)(38,44,46,41)(39,42,47,49)(45,50,51,48);(30,34)(32,35)(36,38,40,46)(37,41,43,44)(39,45,47,51)(42,48,49,50);(21,24)(25,27)(28,30)(29,32)(31,34)(33,35)(36,39,40,47)(37,42,43,49)(38,45,46,51)(41,48,44,50);(29,33)(30,34)(39,47)(42,49)(45,51)(48,50);(20,22,23,26)(21,25,24,27)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 29667);