Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of (C3×A4)⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C22×C32 |
| direct product | C4×(C3×A4)⋊A4 |
| unambiguous semidirect product | (C3×C4×A4)⋊A4 |
| Sylow | C24×C4 ⋊ H(3,𝔽3) |
462 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | C4×(C22⋊A4)⋊H(3,𝔽3) |
| maximal normal subgroup of | C4×(C22⋊A4)⋊H(3,𝔽3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30329);