Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C11×#428 ⋊ C2 |
| Sylow | C11 ⋊ #3356 |
342 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=e,b^2=g,c^2=eg,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,c^b=cg,d^b=de,h^b=h^10,f^c=fg139 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#3356, C2×#13081227, #15632531, … |
| maximal normal subgroup of | D11×#3356, C2×#13081227, #15632531, … |
| maximal quotient of | #14770218, #14770240, #14771535, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 17121);