Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C32 · Schur multiplier (H2) = C25×C3 |
| direct product | C2×C32×#932 |
| Fitting | C22×C33×D4 ⋊ C2 |
| Sylow | C33 ⋊ C2×AGL(1,ℤ/8) |
2732 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
378 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×#10595100, C3×AGL(1,𝔽7)×#932, C2×C32×#5077, … |
| maximal normal subgroup of | C2×C3×#10595100, C2×C32×#5077, C2×C3×#10591522 |
| maximal quotient of | C3×AGL(1,𝔽7)×#932 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 45239);