Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of C82⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C33×C8 |
| direct product | C32×C82⋊C3 |
| unambiguous semidirect product | C82⋊C33 |
| unambiguous semidirect product | (C3×C82)⋊C32 |
| Fitting | C32×C82 ⋊ C3 |
| derived, Sylow | C82 ⋊ C33 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C82⋊C3 |
| commutator, cosocle, hypocenter | C82 | C33 |
| Frattini | C42 | C32×A4 |
| Fitting | C32×C82 | C3 |
| socle | C22×C32 | C42⋊C3 |
| LCS | G ▷ C82 | |
| UCS | C1 ◁ C32 | |
178 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 11809);