Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of D13⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24 |
| direct product | C22×D13⋊A4 |
| unambiguous semidirect product | D13⋊(C22×A4) |
| unambiguous semidirect product | (C22⋊(C13⋊C3))⋊C23 |
| unambiguous semidirect product | (C2×C22⋊(C13⋊C3))⋊C22 |
| Fitting, socle | C24×C13 ⋊ C2×C3 |
| derived | C22×C13 ⋊ C23×C3 |
| Hall | C24×D13 ⋊ C3 |
| Sylow | C13 ⋊ C23×A4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D13⋊A4 |
| commutator, cosocle, hypocenter | C22×C13 | C23×C3 |
| Frattini | C1 | G |
| Fitting, socle | C24×C13 | C2×C3 |
| LCS | G ▷ C22×C13 | |
| UCS | C1 ◁ C22 | |
356 conjugacy classes of subgroups.
| transitive degree | μt(G) = 156 |
64 conjugacy classes — view the full character table.
| maximal subgroup of | C22×A4×D13⋊C3, #72242025, A4×D13⋊A4, … |
| maximal normal subgroup of | C22×A4×D13⋊C3, #72242025, A4×D13⋊A4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1446);