Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#10622773 |
| Fitting | C22×C11×D8 ⋊ C2 |
| Sylow | C11 ⋊ C2×#472 |
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 352 |
172 conjugacy classes — view the full character table.
| maximal subgroup of | #14670735, #14670741, #14670798, … |
| maximal normal subgroup of | #14670735, #14670741, #14670798, … |
| maximal quotient of | C2×#13067968, C2×#13068012, C2×#13068022, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 14214);