Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of C9⋊SL(2,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C8 · Schur multiplier (H2) = C32 |
| direct product | C8×Q8⋊H(3,𝔽3) |
| unambiguous semidirect product | (C8×Q8)⋊H(3,𝔽3) |
| unambiguous semidirect product | (C3×C8×SL(2,𝔽3))⋊C3 |
| Fitting | C32×C8×Q8 ⋊ C3 |
| Sylow | C8×Q8 ⋊ H(3,𝔽3) |
237 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 237 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
248 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 7318);