Finite Group DatabasebetaFinite Group Databasebeta| order | 17344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C271 ⋊ #391 |
186 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17344 |
Polycyclic presentation:
2^6,271|a^2=f,b^2=def,c^2=e,b^a=bd,c^a=ce,g^a=g^270,g^b=g^2702728 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46834490, #46836323, #46836325, … |
| maximal normal subgroup of | #46834490, #46836323, #46836325, … |
| maximal quotient of | #46834593, #46834596, #46834617, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17344, 456);