Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C19 ⋊ #339 |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 304 |
Polycyclic presentation:
2^6,19|a^2=d,b^2=e,c^2=f,b^a=bc,c^a=cf,e^a=ef,g^a=g^18316 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#339, C2×#11926304, #14563343, … |
| maximal normal subgroup of | D19×#339, C2×#11926304, #14563343, … |
| maximal quotient of | #14561468, #14561472, #14561475, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 309);