Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C19 ⋊ #358 |
58 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1216 |
Polycyclic presentation:
2^6,19|a^2=d,b^2=f,c^2=ef,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^18,c^b=ce,e^b=ef148 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#358, C2×#11926348, #14565341, … |
| maximal normal subgroup of | D19×#358, C2×#11926348, #14565341, … |
| maximal quotient of | #14561599, #14561647, #14561684, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 353);