Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C39 |
| direct product | C3×(C3×C37⋊C3)⋊H(3,𝔽3) |
| Fitting | C32×H(3,𝔽3)×C37 ⋊ C3 |
| Sylow | C37 ⋊ C3×C32⋊H(3,𝔽3) |
3824 conjugacy classes of subgroups; only the 382 normal subgroups are shown.
This group has 3824 conjugacy classes of subgroups — too many to draw. Only its 382 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2997 |
1341 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 3302);