Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C71 ⋊ #7178 |
274 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18176 |
Polycyclic presentation:
2^8,71|a^2=d,b^2=e,c^2=f,d^2=g,e^2=fgh,f^2=h,b^a=bc,c^a=cf,e^a=efh,f^a=fh,i^a=i^70,c^b=ch,d^b=dh2864 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 56504);