Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| automorphism | ? |
| homology | Abelianization (H1) = C92 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting | C3×C27×C37 ⋊ C9 |
| Sylow | C37 ⋊ #10624472 |
170 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 60 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=d,b^3=e,c^3=f^2,e^3=f,b^a=bc,c^a=cf,e^a=ef^2,g^a=g^34,d^b=df,g^d=g^10429 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 4104);