Finite Group DatabasebetaFinite Group Databasebeta| order | 7006 |
| isoclinism | isoclinic class of D31 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C113 · Schur multiplier (H2) = C1 |
| direct product | D31×C113 |
| unambiguous semidirect product | C31⋊(C2×C113) |
| Fitting, socle, Hall | C31×C113 ⋊ C2 |
| derived, Sylow | C31 ⋊ C2×C113 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C113 | D31 |
| commutator, hypocenter | C31 | C2×C113 |
| Frattini | C1 | G |
| Fitting, socle | C31×C113 | C2 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C113 | |
8 conjugacy classes of subgroups.
1921 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D31×D113, C2×D31×C113, C3×D31×C113, … |
| maximal normal subgroup of | D31×D113, C2×D31×C113, C3×D31×C113, … |
| maximal quotient of | C113×Dic31, C2×D31×C113, C3×D31×C113, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7006, 1);