Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of C9⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C42 · Schur multiplier (H2) = C2×C32×C4 |
| direct product | C42×C22⋊H(3,𝔽3) |
| Fitting | C22×C32×C42 ⋊ C3 |
| Sylow | C22×C42 ⋊ H(3,𝔽3) |
768 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 150 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
320 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 18225);