Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C71×#2285 ⋊ C2 |
| Sylow | C71 ⋊ #23730 |
1126 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9088 |
Polycyclic presentation:
2^8,71|a^2=e,b^2=ef,d^2=h,e^2=h,f^2=h,b^a=be,c^a=cf,i^a=i^70,c^b=cg,e^b=eh,f^b=fh,i^b=i^70,e^c=eh,f^c=fh,i^c=i^702024 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 199371);