Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C71×#2049 ⋊ C2 |
| Sylow | C71 ⋊ #24423 |
1284 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4544 |
Polycyclic presentation:
2^8,71|a^2=fh,b^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,c^b=cg,f^b=fh,g^b=gh,e^c=eh,f^c=fh,g^c=gh,i^c=i^70,f^d=fh,i^d=i^70845 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 207113);