Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C71 ⋊ C4×SD64 |
202 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 9088 |
Polycyclic presentation:
2^8,71|a^2=e,b^2=h,c^2=e,d^2=fg,f^2=gh,g^2=h,b^a=bd,d^a=df,f^a=fg,g^a=gh,i^a=i^70,d^b=df,f^b=fg,g^b=gh,i^b=i^70,i^c=i^701406 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 90150);