Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Dic19⋊C16 |
| Sylow | C19 ⋊ C4⋊C16 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1216 |
Polycyclic presentation:
2^6,19|a^2=d,b^2=c,d^2=e,e^2=f,b^a=bc,g^b=g^18328 conjugacy classes — view the full character table.
| maximal subgroup of | D19×C4⋊C16, C2×Dic19⋊C16, #14565389, … |
| maximal normal subgroup of | D19×C4⋊C16, C2×Dic19⋊C16, #14565389, … |
| maximal quotient of | #14561698, #14561704, #14561712, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 367);