Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C32 · Schur multiplier (H2) = C25×C3 |
| direct product | C32×#5835 |
| Fitting | C33×H(5,𝔽2) ⋊ C2 |
| Sylow | C33 ⋊ #576 |
2272 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
351 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#13164434, #72253017 |
| maximal normal subgroup of | #72253017 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 45275);