Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C11×#427 ⋊ C2 |
| Sylow | C11 ⋊ #3347 |
360 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=e,c^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,d^b=de,h^b=h^10,f^c=fg169 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#3347, C2×#13081112, #15632431, … |
| maximal normal subgroup of | D11×#3347, C2×#13081112, #15632431, … |
| maximal quotient of | #14770072, #14770162, #14771462, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 17006);