Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18316 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18331 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3460 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
998 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,26,32)(22,34,36,47)(23,30,24,40)(25,31,27,33)(28,41,45,35)(29,39,42,38)(37,44,43,51)(46,50,48,49);(20,22)(21,28)(23,35)(24,41)(25,43)(26,36)(27,37)(29,44)(30,47)(31,48)(32,45)(33,46)(34,40)(38,50)(39,49)(42,51);(20,21,27,33)(22,28,37,46)(23,29,39,40)(24,42,38,30)(25,31,26,32)(34,35,44,49)(36,45,43,48)(41,51,50,47);(20,23,26,24)(21,29,32,42)(22,35,36,41)(25,38,27,39)(28,44,45,51)(30,33,40,31)(34,48,47,46)(37,49,43,50)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11319);