Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C11×#386 ⋊ C2 |
| Sylow | C11 ⋊ C4×#121 |
824 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=g,b^2=e,d^2=g,b^a=be,c^a=cf,h^b=h^10,h^d=h^10196 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D11×#121, C2×#13071126, C4×#10623117, … |
| maximal normal subgroup of | C4×D11×#121, C2×#13071126, C4×#10623117, … |
| maximal quotient of | #14674917, Dic11×#386, #14674928, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 7020);