Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C33 |
| unambiguous semidirect product | (C37⋊C3)⋊#6873 |
| Sylow | C37 ⋊ C3×#6873 |
320 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2997 |
Polycyclic presentation:
3^6,37|a^3=e,e^3=f^2,b^a=bd,d^a=df,g^a=g^16,d^b=df,g^c=g^10,g^e=g^26285 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 4290);