Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C67×#2166 ⋊ C2 |
| Sylow | C67 ⋊ #11989 |
292 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2144 |
Polycyclic presentation:
2^8,67|a^2=e,c^2=g,d^2=g,e^2=fg,f^2=h,b^a=bd,c^a=cf,d^a=df,f^a=fh,g^a=gh,i^a=i^66,d^b=dg,e^b=efgh,f^b=fh,i^b=i^66,d^c=dh1090 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 81086);