Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of S4×D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
| direct product | C2×S4×D13 |
| unambiguous semidirect product | (C13×S4)⋊C22 |
| unambiguous semidirect product | (A4⋊D13)⋊C22 |
| unambiguous semidirect product | (A4×D13)⋊C22 |
| Fitting, socle | C23×C13 ⋊ C2×D3 |
| derived | A4×C13 ⋊ C23 |
| Sylow | C13 ⋊ C22×S4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | S4×D13 |
| commutator, cosocle, hypocenter | A4×C13 | C23 |
| Frattini | C1 | G |
| Fitting, socle | C23×C13 | C2×D3 |
| LCS | G ▷ A4×C13 | |
| UCS | C1 ◁ C2 | |
262 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 78 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | D3×S4×D13, C2×S4×D13⋊C3, D13×GL(2,ℤ/4), … |
| maximal normal subgroup of | C2×S4×D13⋊C3, D13×GL(2,ℤ/4), C2×S4×#261, … |
| maximal quotient of | D3×S4×D13, D13×GL(2,ℤ/4) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1438);