Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#36881 |
| 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 | |
1500 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)(28,29,31,33)(30,32,34,35)(36,37)(38,42)(39,41)(40,47)(43,48)(44,46)(45,50)(49,51);(21,24)(25,27)(37,39)(42,44)(43,47)(49,50);(20,21)(22,25)(23,24)(26,27)(28,29)(30,32)(31,33)(34,35)(36,38,41,46)(37,42,39,44)(40,45,48,51)(43,49,47,50);(20,21)(22,25)(23,24)(26,27)(36,39,41,37)(38,44,46,42)(40,47,48,43)(45,50,51,49);(20,22)(21,25)(23,26)(24,27)(28,30,31,34)(29,32,33,35)(36,40)(37,43)(38,45)(39,47)(41,48)(42,49)(44,50)(46,51)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 29869);