Finite Group DatabasebetaFinite Group Databasebeta| order | 5332 |
| isoclinism | isoclinic class of D31 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×Dic31 |
| unambiguous semidirect product | C31⋊(C4×C43) |
| derived, Sylow | C31 ⋊ C4×C43 |
| Hall | C31×C43 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C43 | D31 |
| commutator, hypocenter | C31 | C4×C43 |
| Frattini | C2 | C43×D31 |
| Fitting, socle | C2×C31×C43 | C2 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C2×C43 | |
12 conjugacy classes of subgroups.
1462 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C43×Dic31, C43×Dic93, Dic31×C43⋊C3, … |
| maximal normal subgroup of | C3×C43×Dic31, Dic31×C43⋊C3, C43×(C31⋊C3)⋊C4, … |
| maximal quotient of | C3×C43×Dic31, C43×Dic93, C5×C43×Dic31, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5332, 2);