Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C32 · Schur multiplier (H2) = C29×C3 |
| direct product | C2×C32×#1004 |
| Fitting | C22×C33×D4 ⋊ C2 |
| Sylow | C33 ⋊ C2×H(5,𝔽2) |
6332 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
486 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×#10596675, C2×C32×#5077, C2×C3×#10591510 |
| maximal normal subgroup of | C2×C3×#10596675, C2×C32×#5077, C2×C3×#10591510 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 47779);