Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of #634 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C27×C3 |
| direct product | C22×C3×#3757 |
| Sylow | C33 ⋊ C22×C22⋊C4 |
7036 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
504 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×C3×#64162, C22×C3⋊(#1094⋊C4) |
| maximal normal subgroup of | C22×C3×#64162 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 45653);