Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C269 ⋊ Q8⋊C8 |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17216 |
Polycyclic presentation:
2^6,269|a^2=d,b^2=e,c^2=e,d^2=f,b^a=bc,c^a=ce,g^a=g^268,c^b=ce,g^b=g^2684316 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Q8⋊C8×D269, C2×#31770337, #46809264, … |
| maximal normal subgroup of | Q8⋊C8×D269, C2×#31770337, #46809264, … |
| maximal quotient of | #46808709, #46808710, #46808725, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 281);