Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C2×#10622447 |
| Fitting | C2×C11×C4⋊C8 ⋊ C2 |
| Sylow | C11 ⋊ C2×C8×D4 |
616 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 253 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 704 |
280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #14644330, #14644340, #14644534, … |
| maximal normal subgroup of | #14644330, #14644340, #14644534, … |
| maximal quotient of | C2×#13067410, C2×#13067415, C2×#13067422, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13182);