Finite Group DatabasebetaFinite Group Databasebeta| order | 11532 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C31 |
| direct product | C3×#16838652 |
| Fitting, socle, Hall | C3×C312 ⋊ C4 |
| derived, Sylow | C312 ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #16838652 |
| commutator, hypocenter | C312 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C312 | C4 |
| prime radical | C3×C31⋊D31 | C2 |
| cosocle | C31⋊D31 | C2×C3 |
| LCS | G ▷ C312 | |
| UCS | C1 ◁ C3 | |
76 conjugacy classes of subgroups.
732 conjugacy classes — view the full character table.
| maximal subgroup of | #16838652⋊C9, C9×#16838652, C3×#26040355, … |
| maximal normal subgroup of | #16838652⋊C9, C9×#16838652, C3×#16838652⋊C3, … |
| maximal quotient of | C9×#16838652, C32×#16838652, C3×C3⋊#16838652 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11532, 49);