Finite Group DatabasebetaFinite Group Databasebeta| order | 17344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C271 ⋊ #470 |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8672 |
Polycyclic presentation:
2^6,271|a^2=f,b^2=df,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^270,c^b=cf2716 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46834351, #46834353, #46834357, … |
| maximal normal subgroup of | #46834351, #46834353, #46834357, … |
| maximal quotient of | #46835853, #46835858, #46835887, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17344, 807);