Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of C9⋊SL(2,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C34 |
| direct product | C9×Q8⋊H(3,𝔽3) |
| Fitting | C32×Q8×C9 ⋊ C3 |
| Sylow | Q8 ⋊ C9×H(3,𝔽3) |
353 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 353 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 648 |
279 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1629);