Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #368×C173 ⋊ C2 |
| Sylow | C173 ⋊ #2161 |
140 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5536 |
Polycyclic presentation:
2^7,173|a^2=e,b^2=df,d^2=fg,e^2=g,f^2=g,b^a=bd,d^a=df,f^a=fg,c^b=cg,h^c=h^1721924 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 6303);