Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18376 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18383 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C22×D4×C19 | D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
986 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)(22,32,36,48)(23,29,24,39)(26,31,42,49)(27,33,45,34)(28,38,40,41)(35,43,37,47)(44,50,46,51);(20,22,25,36)(21,27,30,45)(23,34,24,33)(26,37,42,35)(28,47,40,43)(29,48,39,32)(31,46,49,44)(38,50,41,51);(20,21)(22,27)(23,28)(24,40)(25,30)(26,31)(29,41)(32,50)(33,43)(34,47)(35,44)(36,45)(37,46)(38,39)(42,49)(48,51);(20,23,25,24)(21,28,30,40)(22,33,36,34)(26,38,42,41)(27,43,45,47)(29,31,39,49)(32,46,48,44)(35,50,37,51)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11371);