Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C173 ⋊ #1318 |
170 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 34 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=d,c^2=g,d^2=f,b^a=bc,c^a=ce,e^a=eg,h^a=h^80,c^b=cg,d^b=deg,h^b=h^172,d^c=dg,h^d=h^1721402 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 19439);