Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#10622344 |
| Fitting | C2×C11×C22⋊C8 ⋊ C2 |
| Sylow | C11 ⋊ C2×#450 |
996 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 352 |
238 conjugacy classes — view the full character table.
| maximal subgroup of | #14648916, #14648918, #14650191, … |
| maximal normal subgroup of | #14648916, #14648918, #14650191, … |
| maximal quotient of | C2×#13067570, C2×#13067638, C2×#13067587, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13694);