Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C269 ⋊ #339 |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4304 |
Polycyclic presentation:
2^6,269|a^2=d,b^2=e,c^2=f,b^a=bc,c^a=cf,e^a=ef,g^a=g^268,g^b=g^2682708 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #339×D269, C2×#31770366, #46810593, … |
| maximal normal subgroup of | #339×D269, C2×#31770366, #46810593, … |
| maximal quotient of | #46808717, #46808723, #46808724, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 310);