Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C19 ⋊ #366 |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1216 |
Polycyclic presentation:
2^6,19|a^2=d,b^2=ce,c^2=ef,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^18310 conjugacy classes — view the full character table.
| maximal subgroup of | #14561813, #14561814, #14561816, … |
| maximal normal subgroup of | #14561813, #14561814, #14561816, … |
| maximal quotient of | #14561707, #14561727, #14561835, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 375);