Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | Q8×C22⋊Dic11 |
| Sylow | C11 ⋊ Q8×C22⋊C4 |
820 conjugacy classes of subgroups; only the 333 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 333 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 | #14650211, #14650215, #14650239, … |
| maximal normal subgroup of | #14650211, #14650215, #14650239, … |
| maximal quotient of | C4⋊C4×C22⋊Dic11, Q8×C11⋊#95, #14675311, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 7346);