Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#36912 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C19 |
| prime radical | C22×D4×C19 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
1570 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)(29,33)(31,34)(36,37,42,41)(38,45,40,43)(39,47,49,44)(46,50,48,51);(21,24)(25,27)(29,33)(30,35)(36,38,42,40)(37,43,41,45)(39,48,49,46)(44,51,47,50);(20,21)(22,25)(23,24)(26,27)(28,29,32,33)(30,34,35,31)(36,39,42,49)(37,44,41,47)(38,46,40,48)(43,50,45,51);(20,21)(22,25)(23,24)(26,27)(28,30)(29,34)(31,33)(32,35)(36,40,42,38)(37,45,41,43)(39,48,49,46)(44,51,47,50);(20,22)(21,25)(23,26)(24,27)(28,31,32,34)(29,30,33,35)(36,41,42,37)(38,45,40,43)(39,47,49,44)(46,51,48,50)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 29900);