Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #117×C173 ⋊ C4 |
| Sylow | C173 ⋊ C2×H(3,ℤ/4) |
404 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2768 |
Polycyclic presentation:
2^7,173|a^2=e,b^2=f,d^2=g,b^a=bd,f^a=fg,h^a=h^80,e^b=eg,h^c=h^172,h^e=h^172904 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 20180);