Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of D3×C3⋊#1020 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C24×C3 |
| direct product | D3×C3⋊#1020 |
| unambiguous semidirect product | (C3×D3)⋊#1020 |
| Fitting, socle | C24×C32 ⋊ C2×D3 |
| derived | C32×C22⋊A4 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C32×C22⋊A4 | C22 |
| Fitting, socle | C24×C32 | C2×D3 |
| LCS | G ▷ C32×C22⋊A4 | |
| UCS | C1 | |
1182 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 1182 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
54 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 47899);