Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#10622599 |
| Sylow | C11 ⋊ C2×#400 |
604 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 245 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1408 |
244 conjugacy classes — view the full character table.
| maximal subgroup of | #14648805, #14648807, #14648810, … |
| maximal normal subgroup of | #14648805, #14648807, #14648810, … |
| maximal quotient of | C2×#13066869, C2×#13066872, C2×#13066875, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 7762);