Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C71 ⋊ #9547 |
392 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18176 |
Polycyclic presentation:
2^8,71|a^2=f,b^2=dfg,c^2=d,e^2=g,f^2=h,b^a=bd,c^a=ce,e^a=eg,i^a=i^70,c^b=ch,i^b=i^70,e^c=eg2024 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 67785);