Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×SD16×C269 ⋊ C2 |
| Sylow | C269 ⋊ #450 |
188 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4304 |
Polycyclic presentation:
2^6,269|a^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,d^b=df,g^c=g^2681895 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #450×D269, C2×#31770754, #46820099, … |
| maximal normal subgroup of | #450×D269, C2×#31770754, #46820099, … |
| maximal quotient of | #46809835, #46809852, #46809903, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 698);