Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| isoclinism | isoclinic class of Dic22 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C2×C8×Dic22 |
| Sylow | C11 ⋊ C2×C8×Q8 |
440 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1408 |
400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#66888, #14644347, C8×#66880, … |
| maximal normal subgroup of | C8×#66888, #14644347, C8×#66880, … |
| maximal quotient of | C2×C8×C4⋊Dic11, C2×C8×Dic11⋊C4, C4×C8×Dic22, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13431);