Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#10623166 |
| Fitting | C2×C11×C22⋊Q8 ⋊ C2 |
| Sylow | C11 ⋊ C2×#554 |
1200 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
190 conjugacy classes — view the full character table.
| maximal subgroup of | #14645458, #14769947, #14770008, … |
| maximal normal subgroup of | #14645458, #14769947, #14770008, … |
| maximal quotient of | C2×#13071492, C2×#13071495, C2×#13071512, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 18042);