Finite Group DatabasebetaFinite Group Databasebeta| order | 17344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C271 ⋊ #331 |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8672 |
Polycyclic presentation:
2^6,271|a^2=d,c^2=f,d^2=ef,b^a=bc,c^a=ce,g^a=g^270,c^b=cf,d^b=def1909 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46834508, #46834509, #331×D271, … |
| maximal normal subgroup of | #46834508, #46834509, #331×D271, … |
| maximal quotient of | #46834185, #46834247, #46834401, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17344, 293);