Finite Group DatabasebetaFinite Group Databasebeta| order | 7006 |
| isoclinism | isoclinic class of D113 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×D113 |
| unambiguous semidirect product | C113⋊(C2×C31) |
| Fitting, socle, Hall | C31×C113 ⋊ C2 |
| derived, Sylow | C113 ⋊ C2×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D113 |
| commutator, hypocenter | C113 | C2×C31 |
| Frattini | C1 | G |
| Fitting, socle | C31×C113 | C2 |
| LCS | G ▷ C113 | |
| UCS | C1 ◁ C31 | |
8 conjugacy classes of subgroups.
1798 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C31×#90673, C31⋊#90673, D31×D113, … |
| maximal normal subgroup of | C31×#90673, C31⋊#90673, D31×D113, … |
| maximal quotient of | C31×Dic113, C2×C31×D113, C3×C31×D113, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7006, 2);