Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C34 |
| direct product | C3×H(3,𝔽3)⋊#66526 |
| unambiguous semidirect product | (C37⋊C3)⋊(H(3,𝔽3)⋊C9) |
| Fitting | C3×H(3,𝔽3)×C37 ⋊ C9 |
| Sylow | C37 ⋊ C3×H(3,𝔽3)⋊C9 |
680 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 999 |
285 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 4275);