Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| isoclinism | isoclinic class of Dic22 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4 |
| direct product | C2×C4×(C2×D11)⋊C4 |
| Fitting | C22×C42×C11 ⋊ C2 |
| Sylow | C11 ⋊ C2×C4×C22⋊C4 |
1360 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#10622106, #14644284, #14646427, … |
| maximal normal subgroup of | C4×#10622106, #14644284, #14646427, … |
| maximal quotient of | C2×C4×C11⋊#95, C42×(C2×D11)⋊C4, C2×(C2×D11)⋊#95, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6841);