Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C269 ⋊ #501 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17216 |
Polycyclic presentation:
2^6,269|a^2=d,b^2=d,c^2=e,e^2=f,b^a=bd,c^a=ce,e^a=ef,c^b=cf,g^b=g^2681892 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #501×D269, C2×#31771012, #46821406, … |
| maximal normal subgroup of | #501×D269, C2×#31771012, #46821406, … |
| maximal quotient of | #46811050, #46811621, #46811622, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 956);