Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | M16×D13⋊C3 |
| unambiguous semidirect product | (M16×D13)⋊C3 |
| Fitting | C13×M16 ⋊ C2×C3 |
| Hall | M16×D13 ⋊ C3 |
| Hall | C13⋊C3 ⋊ C2×M16 |
| Sylow | C13 ⋊ C2×C3×M16 |
136 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 69 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 | AGL(1,ℤ/8)×D13⋊C3, #104×D13⋊C3, #72229115, … |
| maximal normal subgroup of | AGL(1,ℤ/8)×D13⋊C3, #104×D13⋊C3, #72229115, … |
| maximal quotient of | #72229279, #72259296, #97×D13⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 383);