Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C13 · Schur multiplier (H2) = C22 |
| direct product | D4×A4×C13 |
| unambiguous semidirect product | C4⋊(C2×A4×C13) |
| unambiguous semidirect product | (C22×D4)⋊(C3×C13) |
| Fitting, Hall | C22×D4×C13 ⋊ C3 |
| Sylow | C22×D4 ⋊ C3×C13 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C13 | C22×A4 |
| commutator, cosocle | C23 | C22×C3×C13 |
| Frattini | C2 | C22×A4×C13 |
| Fitting | C22×D4×C13 | C3 |
| socle | C23×C13 | C22×C3 |
| hypercenter | D4×C13 | A4 |
| hypocenter | C22 | C3×D4×C13 |
| LCS | G ▷ C23 ▷ C22 | |
| UCS | C1 ◁ C2×C13 ◁ D4×C13 | |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 156 |
260 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1365);