Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of (C3⋊D3)⋊(C22⋊A4) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C24×C3 |
| unambiguous semidirect product | (C3⋊Dic3)⋊(C22⋊A4) |
| derived | C24×C32 ⋊ C3×C4 |
1495 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 1495 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2,3,2^5,3^2|a^2=c,h^a=h^2,i^a=i^2,d^b=de,e^b=d,f^b=fg,g^b=f,h^b=hi80 conjugacy classes — view the full character table.
| maximal subgroup of | #72242698, C4×(C3⋊D3)⋊(C22⋊A4) |
| maximal normal subgroup of | #72242698, C4×(C3⋊D3)⋊(C22⋊A4) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30727);