Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| direct product | C2×D4×D13⋊C3 |
| unambiguous semidirect product | D13⋊(C2×C3×D4) |
| unambiguous semidirect product | (C2×D4×D13)⋊C3 |
| Fitting | C2×D4×C13 ⋊ C2×C3 |
| Hall | C2×D4×D13 ⋊ C3 |
| Hall | C13⋊C3 ⋊ C22×D4 |
| Sylow | C13 ⋊ C22×C3×D4 |
472 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 175 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 104 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D4×AGL(1,𝔽13), #120×D13⋊C3, #72229010, … |
| maximal normal subgroup of | C2×D4×AGL(1,𝔽13), #120×D13⋊C3, #72229010, … |
| maximal quotient of | #120×D13⋊C3, #127×D13⋊C3, AGL(1,ℤ/8)×D13⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1246);