Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C71×#1281 ⋊ C2 |
| Sylow | C71 ⋊ #7109 |
228 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 63 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|a^2=d,c^2=fh,d^2=g,f^2=h,b^a=bc,c^a=ce,e^a=eh,c^b=cf,d^b=def,f^b=fh,g^b=gh,i^b=i^70,d^c=dh1580 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 56325);