Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C4⋊C8×C173 ⋊ C2 |
| Sylow | C173 ⋊ #1797 |
400 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11072 |
Polycyclic presentation:
2^7,173|a^2=f,b^2=d,f^2=g,b^a=bd,c^a=ce,h^c=h^1723496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 4487);