Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C269 ⋊ #446 |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17216 |
Polycyclic presentation:
2^6,269|a^2=e,b^2=d,c^2=de,e^2=f,b^a=bd,c^a=cf,g^b=g^268,g^c=g^2682708 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #446×D269, C2×#31770734, #46819814, … |
| maximal normal subgroup of | #446×D269, C2×#31770734, #46819814, … |
| maximal quotient of | #46810751, #46810758, #46810762, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 678);