Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | Q16×C22⋊D11 |
| Fitting | C22×C11×Q16 ⋊ C2 |
| Sylow | C11 ⋊ D4×Q16 |
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 704 |
175 conjugacy classes — view the full character table.
| maximal subgroup of | #14910254, #14910255, #14910261, … |
| maximal normal subgroup of | #14910254, #14910255, #14910261, … |
| maximal quotient of | #14743956, #14743961, #14743971, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 16256);