Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | #585×C173 ⋊ C2 |
| Sylow | C173 ⋊ #3584 |
1424 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5536 |
Polycyclic presentation:
2^7,173|e^2=g,f^2=g,b^a=bf,f^a=fg,f^b=fg,h^b=h^172,d^c=dg2968 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 19281);