Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22⋊C4×Dic22 |
| Sylow | C11 ⋊ Q8×C22⋊C4 |
820 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
250 conjugacy classes — view the full character table.
| maximal subgroup of | #14650212, #14650216, #14650240, … |
| maximal normal subgroup of | #14650212, #14650216, #14650240, … |
| maximal quotient of | C22⋊C4×C4⋊Dic11, C22⋊C4×Dic11⋊C4, #95×Dic22, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 7345);