Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C11×#499 ⋊ C2 |
| Sylow | C11 ⋊ #3381 |
338 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=eg,b^2=eg,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=de,f^c=fg,h^c=h^10,h^d=h^10145 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#3381, C2×#13081488, #15634235, … |
| maximal normal subgroup of | D11×#3381, C2×#13081488, #15634235, … |
| maximal quotient of | #14770366, #14770384, #14772175, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 17382);