Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42 |
| direct product | C4×#66945 |
| Fitting | C4×C11×C4⋊C4 ⋊ C2 |
| Sylow | C11 ⋊ C4×#117 |
752 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #14643299, #14643303, #14643347, … |
| maximal normal subgroup of | #14643299, #14643303, #14643347, … |
| maximal quotient of | C4×#10622261, C4×#10622279, C4×C4⋊C4×Dic11, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6850);