Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C71×#2053 ⋊ C2 |
| Sylow | C71 ⋊ #23535 |
1352 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2272 |
Polycyclic presentation:
2^8,71|c^2=e,e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,c^b=cg,e^b=eh,g^b=gh,d^c=dh,i^d=i^70956 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 197487);