Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C210 |
| direct product | C2×C3×D32×D4 |
| Fitting | C2×C33×D4 ⋊ C22 |
| Sylow | C33 ⋊ C23×D4 |
6210 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×#10596675, D32×D4×AGL(1,𝔽7) |
| maximal normal subgroup of | C2×C3×#10596675 |
| maximal quotient of | D32×D4×AGL(1,𝔽7) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 47609);