Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13229 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C2×C42 |
| direct product | C19×#13231 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #1964 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C2×#41 | C23×C19 |
| prime radical | C19×#3058 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C2×C4×C19 ◁ C2×C19×#131 ◁ G | |
468 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)(20,21)(22,24,32,39)(23,33)(25,40)(26,29)(27,36)(28,34)(30,42,45,51)(31,46,43,38)(35,49,50,44)(37,47)(41,48);(20,22,24,29,26,32,39,21)(23,30,35,41,37,45,50,27)(25,31,38,40,34,43,46,28)(33,36,44,42,47,48,49,51);(20,23,34,48,26,37,25,36)(21,27,40,47,29,41,28,33)(22,30,43,49,32,45,31,44)(24,35,46,51,39,50,38,42)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6219);