Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C11×#388 ⋊ C2 |
| Sylow | C11 ⋊ #2293 |
652 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=g,b^2=g,c^2=f,d^2=e,b^a=be,c^a=cf,h^c=h^10,h^d=h^10196 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#2293, C2×#13071076, #14912174, … |
| maximal normal subgroup of | D11×#2293, C2×#13071076, #14912174, … |
| maximal quotient of | #14674881, #14674910, #14674912, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6970);