Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C11 ⋊ #2166 |
122 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|a^2=e,c^2=d,e^2=f,f^2=g,b^a=bd,c^a=cf,d^a=dg,h^a=h^10,c^b=cg,e^b=eg,e^c=eg232 conjugacy classes — view the full character table.
| maximal subgroup of | #14640867, #14640868, #14640869, … |
| maximal normal subgroup of | #14640867, #14640868, #14640869, … |
| maximal quotient of | #14668793, #14668843, #14669111, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6326);