Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C11 ⋊ #1526 |
226 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=e,b^2=f,c^2=g,d^2=g,e^2=f,b^a=bd,d^a=df,h^a=h^10,d^b=dg,e^b=efg178 conjugacy classes — view the full character table.
| maximal subgroup of | #14644781, #14644784, #14644791, … |
| maximal normal subgroup of | #14644781, #14644784, #14644791, … |
| maximal quotient of | #14641728, #14641751, #14642020, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 3105);