Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C269 ⋊ C4⋊C16 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17216 |
Polycyclic presentation:
2^6,269|a^2=d,b^2=c,d^2=e,e^2=f,b^a=bc,g^b=g^2684328 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4⋊C16×D269, C2×#31770423, #46812639, … |
| maximal normal subgroup of | C4⋊C16×D269, C2×#31770423, #46812639, … |
| maximal quotient of | #46808948, #46808954, #46808962, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 367);