Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13402 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#13402 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2034 |
| commutator, Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C2×C19×#472 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ C2×C19×#131 ◁ G | |
404 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,27)(22,32)(23,25)(24,38)(28,43)(29,46)(30,31)(33,51)(34,39)(35,49)(36,50)(37,40)(41,44)(45,47);(20,21)(22,33)(23,30)(24,29)(25,27)(26,31)(28,34)(32,47)(35,45)(36,41)(37,48)(38,42)(39,51)(40,46)(43,50)(44,49);(20,22)(21,28,31,45)(23,35)(24,39)(25,34)(26,36)(27,41,30,33)(29,47,46,43)(32,38)(37,50)(40,49)(42,44,48,51)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6390);