Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×#66898 |
| Sylow | C11 ⋊ C22×#99 |
1112 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 309 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 352 |
244 conjugacy classes — view the full character table.
| maximal subgroup of | #14659115, #14659116, #14659160, … |
| maximal normal subgroup of | #14659115, #14659116, #14659160, … |
| maximal quotient of | C22×#10622163, C22×#10622166, C2×#13066934, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 12963);