Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#36736 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C19 |
| prime radical | C2×C19×#120 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
1782 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1216 |
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)(31,35)(36,37,41,38)(39,44,47,42)(40,43,48,45)(46,50,51,49);(21,24)(25,27)(28,29,32,33)(30,35,34,31)(37,38)(42,44)(43,45)(49,50);(20,21)(22,25)(23,24)(26,27)(28,30)(29,31)(32,34)(33,35)(36,38,41,37)(39,44,47,42)(40,45,48,43)(46,50,51,49);(20,21)(22,25)(23,24)(26,27)(28,29)(30,31)(32,33)(34,35)(36,39)(37,42)(38,44)(40,46)(41,47)(43,49)(45,50)(48,51);(20,22)(21,25)(23,26)(24,27)(28,31)(29,30)(32,35)(33,34)(36,40,41,48)(37,43,38,45)(39,46,47,51)(42,49,44,50)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 29724);