Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of C9⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C4 · Schur multiplier (H2) = C24×C32 |
| direct product | C22×C4×C22⋊H(3,𝔽3) |
| Fitting | C24×C32×C4 ⋊ C3 |
| Sylow | C24×C4 ⋊ H(3,𝔽3) |
1848 conjugacy classes of subgroups; only the 270 normal subgroups are shown.
This group has 1848 conjugacy classes of subgroups — too many to draw. Only its 270 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.
| maximal subgroup of | C4×(C22⋊A4)⋊H(3,𝔽3), C4×#64269⋊C3, C22×C4×(C3⋊D3)⋊A4 |
| maximal normal subgroup of | C4×(C22⋊A4)⋊H(3,𝔽3), C4×#64269⋊C3, C22×C4×(C3⋊D3)⋊A4 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30904);