Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | AGL(1,ℤ/8)×C269 ⋊ C2 |
| Sylow | C269 ⋊ #472 |
108 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 37 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|b^2=df,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^b=g^268,e^c=ef1490 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #472×D269, C2×#31770873, #46820600, … |
| maximal normal subgroup of | #472×D269, C2×#31770873, #46820600, … |
| maximal quotient of | #46810238, #46810243, #46810282, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 817);