Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D19)⋊C16 |
| Fitting | C2×C16×C19 ⋊ C2 |
| Sylow | C19 ⋊ C22⋊C16 |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^6,19|a^2=d,d^2=e,e^2=f,b^a=bc,g^b=g^18328 conjugacy classes — view the full character table.
| maximal subgroup of | D19×C22⋊C16, C2×(C2×D19)⋊C16, #14565244, … |
| maximal normal subgroup of | D19×C22⋊C16, C2×(C2×D19)⋊C16, #14565244, … |
| maximal quotient of | #14561558, #14561574, #14561589, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 328);