Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C33 |
No aliases for this group.
| Fitting | C3×C37×#733 ⋊ C3 |
| Sylow | C37 ⋊ #10624848 |
198 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 52 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=f^2,b^3=e^2,d^3=f^2,b^a=bd,d^a=de,e^a=ef,c^b=cf,d^b=df,g^b=g^10669 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 3168);