Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#36829 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C19 |
| prime radical | C24×C19 | C24 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
1462 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)(22,26)(25,27)(30,34)(33,35)(36,37,41,42)(38,40,45,43)(39,47,49,44)(46,50,51,48);(21,24)(25,27)(28,29,32,31)(30,33,34,35)(37,42)(38,45)(44,47)(46,51);(20,21)(22,25)(23,24)(26,27)(28,30,32,34)(29,33,31,35)(36,38,41,45)(37,43,42,40)(39,46,49,51)(44,50,47,48);(20,21)(22,25)(23,24)(26,27)(28,31,32,29)(30,35,34,33)(36,39,41,49)(37,44,42,47)(38,46,45,51)(40,48,43,50);(20,22)(21,25)(23,26)(24,27)(36,40,41,43)(37,45,42,38)(39,48,49,50)(44,51,47,46)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 29817);