Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C29 |
| direct product | C2×C3×#64306 |
| Fitting | C22×C33×C4 ⋊ C22 |
| Sylow | C33 ⋊ C22×#41 |
4178 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
288 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×#10595100, C2×C3×#10596675, AGL(1,𝔽7)×#64306, … |
| maximal normal subgroup of | C2×C3×#10595100, C2×C3×#10596675, C2×C3×#10590393 |
| maximal quotient of | AGL(1,𝔽7)×#64306 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 47604);