Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C181 ⋊ D4×C16 |
174 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 174 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) = 11584 |
Polycyclic presentation:
2^7,181|a^2=e,c^2=e,e^2=f,f^2=g,b^a=bd,h^a=h^19,h^b=h^180,h^c=h^162,h^e=h^180980 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 20889);