Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | C71⋊#7050 |
| Sylow | C71 ⋊ #7050 |
332 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18176 |
Polycyclic presentation:
2^8,71|a^2=d,b^2=e,c^2=fh,d^2=h,e^2=fgh,b^a=bc,c^a=cf,e^a=efgh,c^b=cg,d^b=dh,i^b=i^702012 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 56180);