Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C173 ⋊ #1332 |
98 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22144 |
Polycyclic presentation:
2^7,173|a^2=d,b^2=g,c^2=eg,d^2=f,e^2=g,b^a=bc,c^a=ce,e^a=eg,c^b=ce,e^b=eg,h^b=h^1722452 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 2473);