Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C71×#2901 ⋊ C2 |
| Sylow | C71 ⋊ #24472 |
1372 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1136 |
Polycyclic presentation:
2^8,71|a^2=f,e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,c^b=cg,e^b=eh,g^b=gh,f^c=fh,g^c=gh,i^c=i^70,e^d=eh1580 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 207843);