Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C71×#2880 ⋊ C2 |
| Sylow | C71 ⋊ #9241 |
712 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4544 |
Polycyclic presentation:
2^8,71|a^2=f,b^2=dfg,d^2=gh,e^2=gh,b^a=bd,c^a=ce,d^a=dg,i^a=i^70,d^b=dh,e^b=egh,f^b=fh,d^c=dgh,e^c=egh,f^c=fgh1793 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 65889);