Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C71 ⋊ #7079 |
218 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 49 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=d,b^2=gh,c^2=fh,e^2=h,f^2=h,b^a=bc,c^a=ce,e^a=eg,f^a=fh,c^b=cf,d^b=defh,e^b=eh,f^b=fh,i^b=i^70,d^c=dgh1154 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 56249);