Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | C2×#10622166 |
| Sylow | C11 ⋊ C2×#324 |
328 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 704 |
244 conjugacy classes — view the full character table.
| maximal subgroup of | #14640735, #14640736, #14640895, … |
| maximal normal subgroup of | #14640735, #14640736, #14640895, … |
| maximal quotient of | C2×#13066439, #14641728, #14641762, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2820);