Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C4×D4×C173 ⋊ C4 |
| Sylow | C173 ⋊ #2293 |
652 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5536 |
Polycyclic presentation:
2^7,173|a^2=g,b^2=g,c^2=f,d^2=e,b^a=be,c^a=cf,h^a=h^93,h^b=h^80,h^g=h^172916 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 20967);