Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C71×#2366 ⋊ C2 |
| Sylow | C71 ⋊ #26888 |
976 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9088 |
Polycyclic presentation:
2^8,71|a^2=e,d^2=ef,e^2=h,f^2=h,b^a=be,c^a=cf,d^a=de,i^a=i^70,c^b=cg,e^b=eh,f^b=fh,e^c=eh,f^c=fh,e^d=eh,f^d=fh1802 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 240119);