Finite Group DatabasebetaFinite Group Databasebeta| order | 7068 |
| isoclinism | isoclinic class of D31 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C19 · Schur multiplier (H2) = C1 |
| direct product | C3×C19×Dic31 |
| derived, Sylow | C31 ⋊ C3×C4×C19 |
| Hall | C3×C19×C31 ⋊ C4 |
| Hall | C19×C31 ⋊ C3×C4 |
| Hall | C3×C31 ⋊ C4×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C19 | D31 |
| commutator, hypocenter | C31 | C3×C4×C19 |
| Frattini | C2 | C3×C19×D31 |
| Fitting, socle | C2×C3×C19×C31 | C2 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C2×C3×C19 | |
24 conjugacy classes of subgroups.
1938 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×C19×Dic31, C19×Dic31⋊C9, Dic31×#4294, … |
| maximal normal subgroup of | C9×C19×Dic31, C19×Dic31⋊C9, Dic31×#4294, … |
| maximal quotient of | C9×C19×Dic31, C3×C19×Dic93, C32×C19×Dic31, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7068, 6);