Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | AGL(1,ℤ/8)×C269 ⋊ C2 |
| Sylow | C269 ⋊ #453 |
168 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2152 |
Polycyclic presentation:
2^6,269|d^2=f,b^a=bd,c^a=ce,d^a=df,d^b=df,e^b=ef,d^c=df,g^c=g^2681490 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #453×D269, C2×#31770771, #46820231, … |
| maximal normal subgroup of | #453×D269, C2×#31770771, #46820231, … |
| maximal quotient of | #46809801, #46809806, #46809828, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 715);