Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of C13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C32 · Schur multiplier (H2) = C1 |
| direct product | C32×C13⋊C3 |
| unambiguous semidirect product | (C13×C32)⋊C3 |
| Fitting, Hall | C13×C32 ⋊ C3 |
| derived, Sylow | C13 ⋊ C3×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C13⋊C3 |
| commutator, hypocenter | C13 | C3×C32 |
| Frattini | C16 | C2×C13⋊C3 |
| Fitting | C13×C32 | C3 |
| socle | C2×C13 | C3×C16 |
| prime radical | C2×C13⋊C3 | C16 |
| cosocle | C13×C16 | C2×C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C32 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
224 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 2);