Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of C9⋊(C42⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C34×C4 |
| direct product | C3×C32⋊(C42⋊C3) |
| unambiguous semidirect product | (C3×C42)⋊H(3,𝔽3) |
| Fitting | C33×C42 ⋊ C3 |
| Sylow | C42 ⋊ C3×H(3,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center | C32 | C3×C42⋊C3 |
| commutator, cosocle | C3×C42 | C33 |
| Frattini | C22×C3 | C32×A4 |
| Fitting | C33×C42 | C3 |
| socle | C22×C32 | C3×A4 |
| hypercenter | C33 | C42⋊C3 |
| hypocenter | C42 | C3×H(3,𝔽3) |
| LCS | G ▷ C3×C42 ▷ C42 | |
| UCS | C1 ◁ C32 ◁ C33 | |
280 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1506);