Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#10622159 |
| Fitting | C2×C11×Q32 ⋊ C2 |
| Sylow | C11 ⋊ C2×SD64 |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
148 conjugacy classes — view the full character table.
| maximal subgroup of | #14674349, C4×#10622159, #14674362, … |
| maximal normal subgroup of | #14674349, C4×#10622159, #14674362, … |
| maximal quotient of | C2×#13066793, C2×#13066797, C2×#13066817, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6810);