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 ⋊ #449 |
162 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8608 |
Polycyclic presentation:
2^6,269|c^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,d^b=df,g^b=g^268,g^c=g^2681895 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #449×D269, C2×#31770749, #46820099, … |
| maximal normal subgroup of | #449×D269, C2×#31770749, #46820099, … |
| maximal quotient of | #46809813, #46809830, #46809881, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 693);