Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of C3⋊(C3⋊D3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2×C33 |
| direct product | C2×C3⋊(C3⋊(C3⋊C16)) |
| unambiguous semidirect product | (C2×C3)⋊(C3⋊(C3⋊C16)) |
| derived, Sylow | C33 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | C3⋊(C3⋊D3) |
| commutator, hypocenter | C33 | C2×C16 |
| Frattini | C8 | C2×C3⋊(C3⋊D3) |
| Fitting | C2×C33×C8 | C2 |
| socle, prime radical | C22×C33 | C8 |
| cosocle | C33×C8 | C22 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C2×C8 | |
392 conjugacy classes of subgroups.
| transitive degree | μt(G) = 864 |
240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2148);