Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| direct product | C2×C3×#63926 |
| Fitting | C2×C33×D4 ⋊ C22 |
| Sylow | C33 ⋊ C22×D8 |
1794 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
198 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×#10595100, AGL(1,𝔽7)×#63926 |
| maximal normal subgroup of | C2×C3×#10595100 |
| maximal quotient of | AGL(1,𝔽7)×#63926 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 40865);