Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#10623169 |
| Fitting | C2×C11×C22⋊Q8 ⋊ C2 |
| Sylow | C11 ⋊ C2×#539 |
1144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
184 conjugacy classes — view the full character table.
| maximal subgroup of | #14719805, #14719924, #14912854, … |
| maximal normal subgroup of | #14719805, #14719924, #14912854, … |
| maximal quotient of | C2×#13071215, C2×#13071248, C2×#13071251, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 17860);