Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C19 ⋊ #382 |
154 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1216 |
Polycyclic presentation:
2^6,19|a^2=f,b^2=e,c^2=d,b^a=bd,c^a=ce,g^b=g^18,g^c=g^18208 conjugacy classes — view the full character table.
| maximal subgroup of | #14561578, #14563643, #14563644, … |
| maximal normal subgroup of | #14561578, #14563643, #14563644, … |
| maximal quotient of | #14561861, #14561864, #14561891, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 414);