Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| unambiguous semidirect product | D181⋊#327 |
| Fitting | #121×C181 ⋊ C4 |
| Sylow | C181 ⋊ C2×#327 |
388 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2896 |
Polycyclic presentation:
2^7,181|a^2=e,d^2=g,b^a=bd,d^a=df,h^a=h^162,d^b=dg,e^b=efg,h^c=h^180,h^e=h^180668 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 19876);