Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C269 ⋊ #344 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4304 |
Polycyclic presentation:
2^6,269|a^2=d,b^2=e,e^2=f,b^a=bc,c^a=cf,d^b=df,g^b=g^2682702 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #344×D269, C2×#31770375, #46810686, … |
| maximal normal subgroup of | #344×D269, C2×#31770375, #46810686, … |
| maximal quotient of | #46808729, #46808733, #46808734, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 319);