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×#18323 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3459 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1008 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)(20,21,25,30)(22,32,35,47)(23,29,24,38)(26,31,42,48)(27,39,45,33)(28,37,40,41)(34,50,36,43)(44,49,46,51);(20,22)(21,27)(23,33)(24,39)(25,35)(26,36)(28,43)(29,47)(30,45)(31,46)(32,38)(34,42)(37,49)(40,50)(41,51)(44,48);(20,21)(22,27)(23,28)(24,40)(25,30)(26,31)(29,41)(32,49)(33,43)(34,44)(35,45)(36,46)(37,38)(39,50)(42,48)(47,51);(20,23,25,24)(21,28,30,40)(22,33,35,39)(26,37,42,41)(27,43,45,50)(29,31,38,48)(32,44,47,46)(34,51,36,49)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11311);