Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C11×#441 ⋊ C2 |
| Sylow | C11 ⋊ #3401 |
368 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|b^2=e,c^2=e,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^10,c^b=cg,d^b=de,f^c=fg,h^d=h^10139 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#3401, C2×#13081683, #15634816, … |
| maximal normal subgroup of | D11×#3401, C2×#13081683, #15634816, … |
| maximal quotient of | #14770645, #14770664, #14772651, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 17577);