Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#10622154 |
| Fitting | C2×C11×M32 ⋊ C2 |
| Sylow | C11 ⋊ C2×#361 |
256 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 352 |
232 conjugacy classes — view the full character table.
| maximal subgroup of | #14669025, C4×#10622154, #14669044, … |
| maximal normal subgroup of | #14669025, C4×#10622154, #14669044, … |
| maximal quotient of | C2×#13066584, #14663549, #14663780, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6251);