Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#10622859 |
| Sylow | C11 ⋊ C2×#456 |
708 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 352 |
202 conjugacy classes — view the full character table.
| maximal subgroup of | #14671117, #14671127, #14672808, … |
| maximal normal subgroup of | #14671117, #14671127, #14672808, … |
| maximal quotient of | C2×#13067579, C2×#13067613, C2×#13067585, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13852);