Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C71×#2199 ⋊ C2 |
| Sylow | C71 ⋊ #13678 |
400 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2272 |
Polycyclic presentation:
2^8,71|c^2=h,d^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dh,f^a=fg,d^b=dh,e^b=efgh,g^b=gh,i^b=i^70,d^c=df,f^c=fh,g^c=gh,e^d=egh,f^d=fh,f^e=fh617 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 90305);