Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#10622179 |
| Sylow | C11 ⋊ C2×#354 |
284 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 352 |
166 conjugacy classes — view the full character table.
| maximal subgroup of | #14641500, #14641501, #14641524, … |
| maximal normal subgroup of | #14641500, #14641501, #14641524, … |
| maximal quotient of | C2×#13066550, C2×#13066560, #14663051, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6171);