Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×Q8×Dic22 |
| Sylow | C11 ⋊ C2×Q82 |
1112 conjugacy classes of subgroups; only the 621 normal subgroups are shown.
This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 621 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1408 |
250 conjugacy classes — view the full character table.
| maximal subgroup of | #14645539, #14645540, #14645542, … |
| maximal normal subgroup of | #14645539, #14645540, #14645542, … |
| maximal quotient of | C2×Q8×Dic11⋊C4, C2×C4⋊C4×Dic22, C2×Q8×C4⋊Dic11, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 18086);