Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #126⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C2×C33 |
| direct product | C32×#126⋊C3 |
| unambiguous semidirect product | #126⋊C33 |
| unambiguous semidirect product | (C3×#126)⋊C32 |
| Fitting | C32×#126 ⋊ C3 |
| derived | C42 ⋊ C2×C33 |
| Sylow | #126 ⋊ C33 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | #126⋊C3 |
| commutator, cosocle, hypocenter | C42 | C2×C33 |
| Frattini | C22 | C2×C32×A4 |
| Fitting | C32×#126 | C3 |
| socle | C22×C32 | C2×A4 |
| LCS | G ▷ C42 | |
| UCS | C1 ◁ C32 | |
216 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
90 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3700);