Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C11 ⋊ #2274 |
696 conjugacy classes of subgroups; only the 389 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 389 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=f,b^2=g,c^2=e,b^a=be,d^a=de,h^a=h^10,c^b=ce268 conjugacy classes — view the full character table.
| maximal subgroup of | #14647233, #14651211, #14651214, … |
| maximal normal subgroup of | #14647233, #14651211, #14651214, … |
| maximal quotient of | #14674856, #14674858, #14675019, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6867);