Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C181 ⋊ C8×D8 |
196 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 11584 |
Polycyclic presentation:
2^7,181|a^2=e,c^2=e,d^2=f,e^2=g,b^a=bd,d^a=df,h^a=h^19,d^b=df,h^c=h^162,h^e=h^180686 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 20090);