Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #120×C181 ⋊ C4 |
| Sylow | C181 ⋊ #1913 |
380 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 380 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) = 2896 |
Polycyclic presentation:
2^7,181|a^2=f,b^2=df,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^162,d^b=dg,e^b=eg,f^b=fg,h^b=h^162,d^c=dg,f^c=fg,h^f=h^180659 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 20559);