Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C19 ⋊ #333 |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1216 |
Polycyclic presentation:
2^6,19|a^2=d,b^2=f,c^2=f,d^2=ef,b^a=bc,c^a=ce,g^a=g^18,c^b=cf,d^b=def145 conjugacy classes — view the full character table.
| maximal subgroup of | #14561788, #14561789, D19×#333, … |
| maximal normal subgroup of | #14561788, #14561789, D19×#333, … |
| maximal quotient of | #14561461, #14561518, #14561696, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 298);