Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | #364×C173 ⋊ C2 |
| Sylow | C173 ⋊ #1357 |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2768 |
Polycyclic presentation:
2^7,173|a^2=d,c^2=f,d^2=ef,e^2=g,b^a=bc,c^a=ce,e^a=eg,f^a=fg,c^b=cf,d^b=defg,e^b=eg,h^b=h^1722431 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 2546);