Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C19 ⋊ H(3,ℤ/4) |
94 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,e^a=ef,g^a=g^18,d^b=df,g^b=g^18202 conjugacy classes — view the full character table.
| maximal subgroup of | #14561620, #14561621, #14561623, … |
| maximal normal subgroup of | #14561620, #14561621, #14561623, … |
| maximal quotient of | #14561463, #14561466, #14561489, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 306);