Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | H(5,𝔽2)×C173 ⋊ C4 |
| Sylow | C173 ⋊ #1792 |
620 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1384 |
Polycyclic presentation:
2^7,173|a^2=f,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^80,d^b=dg,e^b=eg,d^c=dg,h^f=h^172763 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 20356);