Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#10623090 |
| Fitting | C2×C4×D4×C11 ⋊ C2 |
| Sylow | C11 ⋊ C2×#559 |
1240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
250 conjugacy classes — view the full character table.
| maximal subgroup of | #14645410, #14720100, #14720102, … |
| maximal normal subgroup of | #14645410, #14720100, #14720102, … |
| maximal quotient of | C2×#13071569, C2×#13071574, C2×#13071585, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 18096);