Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C11 ⋊ #1947 |
256 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 107 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,d^2=g,b^a=bd,c^a=ce,d^a=dg,d^b=dg,h^b=h^10,h^c=h^10178 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#1947, C2×#13069373, #14757233, … |
| maximal normal subgroup of | D11×#1947, C2×#13069373, #14757233, … |
| maximal quotient of | #14652349, #14652366, #14652403, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 5267);