Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #131×C181 ⋊ C4 |
| Sylow | C181 ⋊ #1814 |
256 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 5792 |
Polycyclic presentation:
2^7,181|a^2=f,b^2=d,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^162,h^b=h^180,e^c=eg,f^c=fg,h^f=h^180932 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 20397);