Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×M16×C173 ⋊ C4 |
| Sylow | C173 ⋊ #1757 |
284 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 5536 |
Polycyclic presentation:
2^7,173|a^2=e,b^2=f,c^2=e,e^2=g,b^a=bd,f^a=fg,d^b=dg,h^b=h^80,h^c=h^172,h^f=h^172904 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 20266);