Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C71×#1705 ⋊ C2 |
| Sylow | C71 ⋊ #12364 |
358 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1136 |
Polycyclic presentation:
2^8,71|a^2=f,d^2=f,e^2=g,g^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eg,g^a=gh,d^b=df,e^b=eg,g^b=gh,d^c=dg,e^c=egh,f^c=fh,g^c=gh,i^c=i^701364 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 83325);