Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#10622322 |
| Fitting | C2×C11×#97 ⋊ C2 |
| Sylow | C11 ⋊ C2×#433 |
412 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 189 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 704 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | #14644308, #14646641, #14751915, … |
| maximal normal subgroup of | #14644308, #14646641, #14751915, … |
| maximal quotient of | C2×#13068369, C2×#13068385, C2×#13068476, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13137);