Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C269 ⋊ #361 |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4304 |
Polycyclic presentation:
2^6,269|a^2=d,c^2=e,d^2=f,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^187,c^b=cef,d^b=df,e^b=ef,g^d=g^268485 conjugacy classes — view the full character table.
| maximal quotient of | #46825843, #46825844, #46825875, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 1467);