Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | D4×Dic13⋊C3 |
| unambiguous semidirect product | (D4×Dic13)⋊C3 |
| Hall | D4×Dic13 ⋊ C3 |
| Hall | C13⋊C3 ⋊ C4×D4 |
| Sylow | C13 ⋊ C3×C4×D4 |
188 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 208 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D4×D13⋊C3, #72276142, #72276149 |
| maximal normal subgroup of | C4×D4×D13⋊C3, #72276142, #72276149 |
| maximal quotient of | #72276149 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 408);