Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C4×#66991 |
| Fitting | C2×C4×D4×C11 ⋊ C2 |
| Sylow | C11 ⋊ C4×#121 |
824 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | #14648301, #14648306, #14648321, … |
| maximal normal subgroup of | #14648301, #14648306, #14648321, … |
| maximal quotient of | C4×#10622569, C4×#10622557, C4×#10622834, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 7017);