Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C11×#385 ⋊ C2 |
| Sylow | C11 ⋊ #2322 |
632 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=g,b^2=g,c^2=e,b^a=be,c^a=cf,d^a=de,c^b=ce,h^b=h^10,h^c=h^10184 conjugacy classes — view the full character table.
| maximal subgroup of | #14663037, #14663235, #14759768, … |
| maximal normal subgroup of | #14663037, #14663235, #14759768, … |
| maximal quotient of | #14675018, #14675053, #14675072, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 7178);