Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C71 ⋊ #7364 |
126 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 51 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,b^2=e,c^2=h,d^2=f,f^2=g,g^2=h,b^a=bc,c^a=ce,e^a=eh,i^a=i^70,d^b=deh,d^c=dh2012 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 56971);