Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of S4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C24 |
| direct product | C22×C13×S4 |
| unambiguous semidirect product | A4⋊(C23×C13) |
| unambiguous semidirect product | (C2×A4)⋊(C22×C13) |
| Fitting, socle | C24×C13 ⋊ D3 |
| derived | A4 ⋊ C23×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C13 | S4 |
| commutator, cosocle, hypocenter | A4 | C23×C13 |
| Frattini | C1 | G |
| Fitting, socle | C24×C13 | D3 |
| LCS | G ▷ A4 | |
| UCS | C1 ◁ C22×C13 | |
262 conjugacy classes of subgroups.
| transitive degree | μt(G) = 156 |
260 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1440);