Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#36899 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C19 |
| prime radical | C2×C19×#121 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
1526 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)(38,45)(39,43)(40,42)(41,48)(44,49)(46,50)(47,51);(21,24)(25,27)(36,38,42,39)(37,43,40,45)(41,46,49,47)(44,50,48,51);(20,21)(22,25)(23,24)(26,27)(28,29)(30,32)(31,33)(34,35)(36,39,42,38)(37,43,40,45)(41,47,49,46)(44,50,48,51);(20,21)(22,25)(23,24)(26,27)(36,40,42,37)(38,43,39,45)(41,48,49,44)(46,50,47,51);(20,22)(21,25)(23,26)(24,27)(28,30,31,34)(29,32,33,35)(36,41,42,49)(37,44,40,48)(38,46,39,47)(43,50,45,51)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 29887);