Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of #204 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×C32×#805 |
| Fitting | C2×C33×C42 ⋊ C2 |
| Sylow | C33 ⋊ C2×#104 |
1452 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
540 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×#10590393, C2×C32×#5077, C2×C3×#10590397 |
| maximal normal subgroup of | C2×C3×#10590393, C2×C32×#5077, C2×C3×#10590397 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 28436);