Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | AΣL(1,𝔽16)×C173 ⋊ C2 |
| Sylow | C173 ⋊ #2120 |
264 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 55 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|a^2=e,c^2=g,b^a=bd,d^a=df,f^a=fg,e^b=ef,h^c=h^172,e^d=eg1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 6148);