Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | SD16×C22⋊D11 |
| Fitting | C22×C11×SD16 ⋊ C2 |
| Sylow | C11 ⋊ D4×SD16 |
546 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
175 conjugacy classes — view the full character table.
| maximal subgroup of | D4×SD16×D11, C2×SD16×C22⋊D11, #15629062, … |
| maximal normal subgroup of | D4×SD16×D11, C2×SD16×C22⋊D11, #15629062, … |
| maximal quotient of | #14743236, #14743241, #14743251, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 16200);