Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×Q8×D44 |
| Fitting | C2×C4×Q8×C11 ⋊ C2 |
| Sylow | C11 ⋊ C2×D4×Q8 |
1568 conjugacy classes of subgroups; only the 621 normal subgroups are shown.
This group has 1568 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) = 704 |
250 conjugacy classes — view the full character table.
| maximal subgroup of | #14645499, #14645502, #14645515, … |
| maximal normal subgroup of | #14645499, #14645502, #14645515, … |
| maximal quotient of | C2×Q8×(C2×D11)⋊C4, C2×C4⋊C4×D44, C2×Q8×C4⋊Dic11, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 17985);