Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8603 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#13128 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #117 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| socle | C22×C19 | #432 |
| prime radical | C24×C19 | M16 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C2×C19×#97 ◁ G | |
328 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,23)(24,25,28,33,27,32,35,39,29,26,30,34,36,31,37,38);(24,26,28,33,27,31,35,39,29,25,30,34,36,32,37,38);(21,23)(25,31,26,32)(28,30)(33,39,34,38)(35,37)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6116);