Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
| direct product | C2×#10622137 |
| Sylow | C11 ⋊ C2×M64 |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #14641461, #14641462, #14641463, … |
| maximal normal subgroup of | #14641461, #14641462, #14641463, … |
| maximal quotient of | C2×#13066750, C4×#10622137, C2×C22⋊(C11⋊C32), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6802);