Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C16 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3×C3⋊(C3⋊C16) |
| unambiguous semidirect product | (C2×C3)⋊(C3×C3⋊C16) |
| derived | C32 ⋊ C2×C3×C16 |
| Sylow | C33 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C8 | C3⋊D3 |
| commutator, hypocenter | C32 | C2×C3×C16 |
| Frattini | C8 | C2×C3×C3⋊D3 |
| Fitting | C2×C33×C8 | C2 |
| socle, prime radical | C22×C33 | C8 |
| cosocle | C32×C8 | C22×C3 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C2×C3×C8 | |
256 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2107);