Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C71 ⋊ #12722 |
790 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 790 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1136 |
Polycyclic presentation:
2^8,71|a^2=f,c^2=gh,e^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,i^a=i^70,e^b=eh,f^b=fg,d^c=dh,f^c=fh,f^d=fh1574 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 85170);