Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C19 ⋊ #347 |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 304 |
Polycyclic presentation:
2^6,19|a^2=c,b^2=d,c^2=e,e^2=f,b^a=be,d^a=df,c^b=cf,g^b=g^18202 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#347, C2×#11926321, #14565238, … |
| maximal normal subgroup of | D19×#347, C2×#11926321, #14565238, … |
| maximal quotient of | #14561555, #14561557, #14561714, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 326);