Finite Group DatabasebetaFinite Group Databasebeta| order | 11532 |
| isoclinism | isoclinic class of D93 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×Dic93 |
| unambiguous semidirect product | C3⋊(C31×Dic31) |
| unambiguous semidirect product | C31⋊(Dic3×C31) |
| derived | C3×C31 ⋊ C4×C31 |
| Hall | C3×C312 ⋊ C4 |
| Sylow | C312 ⋊ Dic3 |
| Sylow | C3 ⋊ C31×Dic31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C31 | D93 |
| commutator, hypocenter | C3×C31 | C4×C31 |
| Frattini | C2 | C31×D93 |
| Fitting, socle, prime radical | C2×C3×C312 | C2 |
| cosocle | C2×C3×C31 | C2×C31 |
| LCS | G ▷ C3×C31 | |
| UCS | C1 ◁ C2×C31 | |
84 conjugacy classes of subgroups.
2976 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46829295, C31×Dic279, C31×C3⋊((C31⋊C3)⋊C4), … |
| maximal normal subgroup of | C31×C3⋊((C31⋊C3)⋊C4), C3⋊#26040337, C3⋊#26040338, … |
| maximal quotient of | C31×Dic279, C31×C3⋊Dic93, C3×C31×Dic93 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11532, 31);