Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C269 ⋊ #330 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17216 |
Polycyclic presentation:
2^6,269|a^2=d,b^2=e,c^2=f,d^2=e,b^a=bc,c^a=ce,g^a=g^187,c^b=cf,d^b=def,g^d=g^268689 conjugacy classes — view the full character table.
| maximal quotient of | #46825703, #46825704, #46825761 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 1406);