Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#10622364 |
| Fitting | C2×C11×#101 ⋊ C2 |
| Sylow | C11 ⋊ C2×#413 |
756 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 213 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 352 |
154 conjugacy classes — view the full character table.
| maximal subgroup of | #14668753, #14668759, #14671314, … |
| maximal normal subgroup of | #14668753, #14668759, #14671314, … |
| maximal quotient of | C2×#13066929, C2×#13066933, #14719585, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 12984);