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) = C22×C4 |
| direct product | C19×#13234 |
| 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 | |
464 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)(20,21,26,30,27,31,25,43)(22,24,29,41,35,42,34,32)(23,36,39,45,40,50,38,28)(33,47,44,51,49,46,48,37);(20,22,32,21)(23,33,46,28)(24,30,25,34)(26,29,42,43)(27,35,41,31)(36,38,48,37)(39,44,51,50)(40,49,47,45);(20,23,26,39,27,40,25,38)(21,28,43,50,31,45,30,36)(22,33,29,44,35,49,34,48)(24,37,32,46,42,51,41,47)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6222);