Finite Group DatabasebetaFinite Group Databasebeta| order | 11532 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C31 |
| direct product | C4×#15668333 |
| Fitting, Hall | C4×C312 ⋊ C3 |
| derived, Sylow | C312 ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #15668333 |
| commutator, hypocenter | C312 | C3×C4 |
| Frattini | C2 | C2×#15668333 |
| Fitting | C4×C312 | C3 |
| socle, cosocle | C2×C312 | C2×C3 |
| prime radical | C2×#15668333 | C2 |
| LCS | G ▷ C312 | |
| UCS | C1 ◁ C4 | |
54 conjugacy classes of subgroups.
1292 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C31⋊C32, Dic3×#15668333, C3×C4×#15668333 |
| maximal normal subgroup of | C4×C31⋊C32, C3×C4×#15668333 |
| maximal quotient of | C4×#22575711, Dic3×#15668333, C3×C4×#15668333 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11532, 27);