Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11549 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C22×C4 |
| direct product | C19×#13228 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#99 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C22×Q8 | C23×C19 |
| prime radical | C22×D4×C19 | C2×C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ C2×C4×Q8×C19 ◁ G | |
490 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)(21,23)(24,25,29,33,30,34,27,31)(26,35,37,28,32,36,39,38);(24,26,36,33,30,32,35,31)(25,29,39,28,34,27,37,38);(20,21,22,23)(24,27,30,29)(25,31,34,33)(26,37,32,39)(28,36,38,35)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6216);