Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #7855 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×C22⋊#338 |
| unambiguous semidirect product | C22⋊(C19×#338) |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | C2×C42 |
| commutator | C2×C4 | C2×C42×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C22×C19 | C2×#95 |
| prime radical | C25×C19 | Q8 |
| LCS | G ▷ C2×C4 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ G | |
1294 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 608 |
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)(24,25,27,31,29,32,28,37)(26,33,35,30,36,38,34,39);(24,26,28,35,29,36,27,34)(25,30,31,33,32,39,37,38);(21,23)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3706);