Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C11 ⋊ #2070 |
196 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|a^2=de,b^2=d,c^2=g,d^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,h^a=h^10,c^b=cf,f^b=fg,h^b=h^10,d^c=dg,h^c=h^10133 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#2070, C2×#13070018, #14782496, … |
| maximal normal subgroup of | D11×#2070, C2×#13070018, #14782496, … |
| maximal quotient of | #14658410, #14658424, #14658438, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 5912);