Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C71 ⋊ #7451 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18176 |
Polycyclic presentation:
2^8,71|a^2=d,b^2=eh,c^2=fg,d^2=efg,f^2=gh,g^2=h,b^a=bc,c^a=ce,c^b=cf,d^b=def,f^b=fg,g^b=gh,i^b=i^702849 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 57221);