Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×#99×C173 ⋊ C2 |
| Sylow | C173 ⋊ #3026 |
800 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 145 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2768 |
Polycyclic presentation:
2^7,173|b^a=be,c^a=cf,d^a=dg,h^a=h^172,f^b=fg,e^c=eg,h^c=h^1721921 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 13909);