Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | #104×Dic11 |
| Sylow | C11 ⋊ C4×#104 |
360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 352 |
196 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D11×#104, C2×#104×Dic11, #14751495, … |
| maximal normal subgroup of | C4×D11×#104, C2×#104×Dic11, #14751495, … |
| maximal quotient of | Dic11×D4⋊C8, Dic11×Q8⋊C8, #14644387, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 4317);