Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | #367×C173 ⋊ C2 |
| Sylow | C173 ⋊ #2158 |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11072 |
Polycyclic presentation:
2^7,173|a^2=e,b^2=df,c^2=g,d^2=fg,f^2=g,b^a=bd,d^a=df,f^a=fg,h^b=h^172,h^c=h^1721936 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 6293);