Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#10623262 |
| Fitting | C2×C11×C4⋊Q8 ⋊ C2 |
| Sylow | C11 ⋊ C2×#541 |
1004 conjugacy classes of subgroups; only the 485 normal subgroups are shown.
This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 485 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 704 |
184 conjugacy classes — view the full character table.
| maximal subgroup of | #14646314, #14758927, #14759052, … |
| maximal normal subgroup of | #14646314, #14758927, #14759052, … |
| maximal quotient of | C2×#13071224, C2×#13071261, C2×#13071301, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 17877);