Finite Group DatabasebetaFinite Group Databasebeta| order | 8556 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C31 · Schur multiplier (H2) = C2 |
| direct product | D3×C31×D23 |
| unambiguous semidirect product | (D3×C23)⋊(C2×C31) |
| unambiguous semidirect product | (C3×D23)⋊(C2×C31) |
| unambiguous semidirect product | D69⋊(C2×C31) |
| Fitting, socle, Hall | C3×C23×C31 ⋊ C22 |
| derived, Hall | C3×C23 ⋊ C22×C31 |
| Hall | C23×C31 ⋊ C2×D3 |
| Hall | C3×C31 ⋊ C2×D23 |
| Sylow | C23 ⋊ C2×D3×C31 |
| Sylow | C3 ⋊ C2×C31×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D3×D23 |
| commutator, hypocenter | C3×C23 | C22×C31 |
| Frattini | C1 | G |
| Fitting, socle | C3×C23×C31 | C22 |
| LCS | G ▷ C3×C23 | |
| UCS | C1 ◁ C31 | |
40 conjugacy classes of subgroups.
1209 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×C31×D23, D3×D23×C31⋊C3, C3×D3×C31×D23, … |
| maximal normal subgroup of | D3×D23×C31⋊C3, C3×D3×C31×D23 |
| maximal quotient of | D9×C31×D23, C3×D3×C31×D23, D3×C31×D69, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8556, 21);