Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C11 ⋊ #1943 |
240 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1408 |
Polycyclic presentation:
2^7,11|a^2=f,b^2=f,c^2=e,e^2=g,b^a=bd,c^a=ce,e^a=eg,c^b=cg,h^c=h^10172 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#1943, C2×#13069351, #14757122, … |
| maximal normal subgroup of | D11×#1943, C2×#13069351, #14757122, … |
| maximal quotient of | #14652317, #14652337, #14652435, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 5245);