Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C22 |
| direct product | D4×C22⋊(C13⋊C3) |
| unambiguous semidirect product | C4⋊(C2×C22⋊(C13⋊C3)) |
| unambiguous semidirect product | (C22×D4)⋊(C13⋊C3) |
| unambiguous semidirect product | (D4×C13)⋊A4 |
| Fitting, Hall | C22×D4×C13 ⋊ C3 |
| Sylow | C22×D4 ⋊ C13⋊C3 |
| Sylow | C13 ⋊ D4×A4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×C22⋊(C13⋊C3) |
| commutator, socle, cosocle | C23×C13 | C22×C3 |
| Fitting | C22×D4×C13 | C3 |
| hypercenter | D4 | C22⋊(C13⋊C3) |
| hypocenter | C22×C13 | C3×D4 |
| LCS | G ▷ C23×C13 ▷ C22×C13 | |
| UCS | C1 ◁ C2 ◁ D4 | |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 156 |
100 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1372);