Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C23×C4×C173 ⋊ C4 |
| Sylow | C173 ⋊ C22⋊#95 |
1088 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 206 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=f,b^2=g,b^a=bd,c^a=ce,h^a=h^80,h^f=h^1721432 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 19684);