Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×D4×Dic22 |
| Sylow | C11 ⋊ C2×D4×Q8 |
1568 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
250 conjugacy classes — view the full character table.
| maximal subgroup of | #14645454, #14645457, #14645500, … |
| maximal normal subgroup of | #14645454, #14645457, #14645500, … |
| maximal quotient of | C2×C22⋊C4×Dic22, C2×D4×Dic11⋊C4, C2×D4×C4⋊Dic11, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 17984);