Finite Group DatabasebetaFinite Group Databasebeta| order | 11532 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C31 · Schur multiplier (H2) = C2 |
| direct product | D3×C31×D31 |
| unambiguous semidirect product | (D3×C31)⋊(C2×C31) |
| unambiguous semidirect product | (C3×D31)⋊(C2×C31) |
| unambiguous semidirect product | D93⋊(C2×C31) |
| Fitting, socle, Hall | C3×C312 ⋊ C22 |
| derived | C3×C31 ⋊ C22×C31 |
| Sylow | C312 ⋊ C2×D3 |
| Sylow | C3 ⋊ C2×C31×D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D3×D31 |
| commutator, cosocle, hypocenter | C3×C31 | C22×C31 |
| Frattini | C1 | G |
| Fitting, socle | C3×C312 | C22 |
| LCS | G ▷ C3×C31 | |
| UCS | C1 ◁ C31 | |
100 conjugacy classes of subgroups.
1581 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×C31×D31, D3×#19153449, D3×C31×D31⋊C3, … |
| maximal normal subgroup of | D3×C31×D31⋊C3, D3×D31×C31⋊C3, D3×#19153446, … |
| maximal quotient of | D9×C31×D31, C3×D3×C31×D31, D3×C31×D93, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11532, 50);