Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C269 ⋊ #494 |
122 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17216 |
Polycyclic presentation:
2^6,269|a^2=f,b^2=df,c^2=e,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^2684310 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46808923, #46808933, #46808935, … |
| maximal normal subgroup of | #46808923, #46808933, #46808935, … |
| maximal quotient of | #46810482, #46810495, #46810503, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 929);