Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#10622590 |
| Sylow | C11 ⋊ C2×#382 |
712 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 349 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1408 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | #14659593, #14659596, #14659620, … |
| maximal normal subgroup of | #14659593, #14659596, #14659620, … |
| maximal quotient of | C2×#13066842, C2×#13066845, C4×#10622590, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6896);