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×C22⋊Dic11 |
| 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 | #14643366, #14643378, C2×#13066462, … |
| maximal normal subgroup of | #14643366, #14643378, C2×#13066462, … |
| maximal quotient of | C2×C4×C11⋊#95, C42×C22⋊Dic11, C2×#13066839, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6840);