Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C9 · Schur multiplier (H2) = C37 |
| direct product | C3×H(3,𝔽3)×#66526 |
| unambiguous semidirect product | (C37⋊C3)⋊(C9×H(3,𝔽3)) |
| Fitting | C3×H(3,𝔽3)×C37 ⋊ C9 |
| Sylow | C37 ⋊ C3×C9×H(3,𝔽3) |
1688 conjugacy classes of subgroups; only the 468 normal subgroups are shown.
This group has 1688 conjugacy classes of subgroups — too many to draw. Only its 468 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 999 |
429 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 4408);