Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#10623244 |
| Sylow | C11 ⋊ C2×#559 |
1240 conjugacy classes of subgroups; only the 501 normal subgroups are shown.
This group has 1240 conjugacy classes of subgroups — too many to draw. Only its 501 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 704 |
190 conjugacy classes — view the full character table.
| maximal subgroup of | #14645488, #14645849, #14645853, … |
| maximal normal subgroup of | #14645488, #14645849, #14645853, … |
| maximal quotient of | C2×#13071575, C2×#13071588, C2×#13071681, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 18099);