Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C71 ⋊ #11216 |
682 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9088 |
Polycyclic presentation:
2^8,71|a^2=g,b^2=d,c^2=d,f^2=h,g^2=h,b^a=bd,c^a=ce,e^a=eh,f^a=fh,c^b=cf,e^b=eh,f^b=fh,f^c=fh,g^c=gh,i^c=i^702012 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 77526);