Finite Group DatabasebetaFinite Group Databasebeta| order | 11532 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C31 |
| direct product | D3×C31⋊D31 |
| unambiguous semidirect product | (D3×C31)⋊D31 |
| Fitting, socle, derived, Hall | C3×C312 ⋊ C22 |
| Sylow | C312 ⋊ C2×D3 |
| Sylow | C3 ⋊ C2×C31⋊D31 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C312 | C22 |
| LCS | G ▷ C3×C312 | |
| UCS | C1 | |
340 conjugacy classes of subgroups.
1446 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×C31⋊D31, D3×(C31⋊C3)⋊D31, D3×#19153444, … |
| maximal normal subgroup of | D3×(C31⋊C3)⋊D31, D3×#19153444, D3×#19153443, … |
| maximal quotient of | D9×C31⋊D31, C3×D3×C31⋊D31, D3×C3⋊(C31⋊D31), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11532, 51);