Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#10622854 |
| Fitting | C2×C11×H(5,𝔽2) ⋊ C2 |
| Sylow | C11 ⋊ C2×#453 |
844 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 844 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 176 |
202 conjugacy classes — view the full character table.
| maximal subgroup of | #14671072, #14671082, #14672730, … |
| maximal normal subgroup of | #14671072, #14671082, #14672730, … |
| maximal quotient of | C2×#13067534, C2×#13067539, C2×#13067636, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13834);