Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×(C22⋊#261)⋊C3 |
| unambiguous semidirect product | (D13⋊C3)⋊(C22⋊C4) |
| unambiguous semidirect product | (C2×AGL(1,𝔽13))⋊C22 |
| unambiguous semidirect product | (C2×C22⋊#261)⋊C3 |
| Fitting | C23×C13 ⋊ C3×C4 |
| Hall | C2×C22⋊#261 ⋊ C3 |
| Hall | C13⋊C3 ⋊ C2×C22⋊C4 |
| Sylow | C13 ⋊ C2×C3×C22⋊C4 |
264 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 104 |
68 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D4×AGL(1,𝔽13), #72228996, C22⋊C4×AGL(1,𝔽13), … |
| maximal normal subgroup of | C2×D4×AGL(1,𝔽13), #72228996, C22⋊C4×AGL(1,𝔽13), … |
| maximal quotient of | #72228996, #72229010, #72229036, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1167);