Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C11×#343 ⋊ C2 |
| Sylow | C11 ⋊ #2063 |
228 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|a^2=de,b^2=d,d^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,h^a=h^10,c^b=cf,h^b=h^10,d^c=dg,f^c=fg,h^c=h^10136 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#2063, C2×#13069977, #14782319, … |
| maximal normal subgroup of | D11×#2063, C2×#13069977, #14782319, … |
| maximal quotient of | #14658291, #14658305, #14658319, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 5871);