Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×D4×#261 |
| Fitting | C3×D4×C13 ⋊ C4 |
| Hall | C3×C13 ⋊ C4×D4 |
| Sylow | C13 ⋊ C3×C4×D4 |
188 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 156 |
105 conjugacy classes — view the full character table.
| maximal subgroup of | D4×#14523150, #72241883, D3×D4×#261, … |
| maximal normal subgroup of | D3×D4×#261, C3×D4×AGL(1,𝔽13) |
| maximal quotient of | D4×#14523150, #72241883, C3×#67×#261 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1286);