Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting | C37×C27⋊C3 ⋊ C9 |
| Sylow | C37 ⋊ #10624709 |
198 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 84 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,b^3=d,c^3=f,d^3=f,b^a=bd,d^a=df,g^a=g^34,e^b=ef^2,g^c=g^26,g^e=g^10237 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 4325);