Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C269 ⋊ C4 |
| 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,g^a=g^82,d^b=df,g^b=g^187,g^d=g^268,g^e=g^268692 conjugacy classes — view the full character table.
| maximal quotient of | #46825724, #46825726, #46825731, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 1432);