Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C36 |
| unambiguous semidirect product | (C3×#66526)⋊H(3,𝔽3) |
| Fitting | C3×H(3,𝔽3)×C37 ⋊ C9 |
| Sylow | C37 ⋊ #10624555 |
842 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 842 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 999 |
Polycyclic presentation:
3^6,37|a^3=f,b^3=f,b^a=bd,c^a=ce,g^a=g^12,g^b=g^16,g^f=g^26285 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 4224);