Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C4×Q8×Dic11 |
| Sylow | C11 ⋊ C42×Q8 |
684 conjugacy classes of subgroups; only the 425 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 425 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1408 |
280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic11×Q8⋊C8, #14644382, #14644392, … |
| maximal normal subgroup of | Dic11×Q8⋊C8, #14644382, #14644392, … |
| maximal quotient of | C4×C4⋊C4×Dic11, C4×#10622594, Dic11×#387, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6861);