Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×Q16×C173 ⋊ C2 |
| Sylow | C173 ⋊ #3300 |
386 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11072 |
Polycyclic presentation:
2^7,173|a^2=e,b^2=g,c^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^172,d^b=de,h^b=h^172,f^c=fg,h^d=h^1722443 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 16402);