Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#10622766 |
| Sylow | C11 ⋊ C2×#463 |
564 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 704 |
178 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#10622766, #14759998, #14760063, … |
| maximal normal subgroup of | C4×#10622766, #14759998, #14760063, … |
| maximal quotient of | C2×#13068023, C2×#13068037, C2×#13068051, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13932);