Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×Q16×Dic11 |
| Sylow | C11 ⋊ C2×C4×Q16 |
488 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 245 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1408 |
196 conjugacy classes — view the full character table.
| maximal subgroup of | Dic11×#358, #14668994, Dic11×#362, … |
| maximal normal subgroup of | Dic11×#358, #14668994, Dic11×#362, … |
| maximal quotient of | C2×Q16×C11⋊C8, C2×#13067467, C2×#13067513, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13275);