Finite Group DatabasebetaFinite Group Databasebeta| order | 1584 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×C11⋊(#41⋊C3) |
| unambiguous semidirect product | C11⋊(C3×#41⋊C3) |
| unambiguous semidirect product | #4343⋊C32 |
| unambiguous semidirect product | (C3×#4343)⋊C3 |
| Hall | #4343 ⋊ C32 |
| Sylow | C11 ⋊ C3×#41⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | A4×D11 |
| commutator, cosocle, hypocenter | Q8×C11 | C2×C32 |
| Frattini | C2 | C3×A4×D11 |
| Fitting | C3×Q8×C11 | C2×C3 |
| socle | C2×C3×C11 | C2×A4 |
| LCS | G ▷ Q8×C11 | |
| UCS | C1 ◁ C2×C3 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 528 |
147 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1584, 455);