Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of C13⋊(C42⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C4 |
| direct product | C2×C13⋊(C42⋊C3) |
| unambiguous semidirect product | (C2×C13)⋊(C42⋊C3) |
| unambiguous semidirect product | (C2×C42)⋊(C13⋊C3) |
| Fitting, Hall | C2×C42×C13 ⋊ C3 |
| derived | C42×C13 ⋊ C2×C3 |
| Sylow | C2×C42 ⋊ C13⋊C3 |
| Sylow | C13 ⋊ C2×C42⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C13⋊(C42⋊C3) |
| commutator, cosocle, hypocenter | C42×C13 | C2×C3 |
| Frattini | C22 | C2×C22⋊(C13⋊C3) |
| Fitting | C2×C42×C13 | C3 |
| socle | C23×C13 | A4 |
| LCS | G ▷ C42×C13 | |
| UCS | C1 ◁ C2 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 156 |
144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 862);