Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C71 ⋊ #13544 |
212 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4544 |
Polycyclic presentation:
2^8,71|a^2=dg,b^2=de,c^2=d,d^2=h,f^2=gh,g^2=h,b^a=bd,c^a=ce,e^a=eh,i^a=i^70,c^b=cf,f^b=fg,g^b=gh,i^b=i^70,f^c=fg,g^c=gh,i^c=i^701580 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 89728);