Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C19 ⋊ #352 |
68 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 304 |
Polycyclic presentation:
2^6,19|a^2=d,b^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^18,d^b=de,g^b=g^18,d^c=df112 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#352, C2×#11926335, #14565273, … |
| maximal normal subgroup of | D19×#352, C2×#11926335, #14565273, … |
| maximal quotient of | #14561564, #14561582, #14561636, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 340);