Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C173 ⋊ #1290 |
136 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11072 |
Polycyclic presentation:
2^7,173|a^2=d,b^2=e,c^2=fg,d^2=f,e^2=fg,b^a=bc,c^a=cf,e^a=efg,h^a=h^80,d^b=dg,h^d=h^1721408 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 19375);