Finite Group DatabasebetaFinite Group Databasebeta| order | 7068 |
| isoclinism | isoclinic class of D57 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×Dic57 |
| unambiguous semidirect product | C3⋊(C31×Dic19) |
| unambiguous semidirect product | C19⋊(Dic3×C31) |
| derived, Hall | C3×C19 ⋊ C4×C31 |
| Hall | C3×C19×C31 ⋊ C4 |
| Hall | C19×C31 ⋊ Dic3 |
| Hall | C3×C31 ⋊ Dic19 |
| Sylow | C19 ⋊ Dic3×C31 |
| Sylow | C3 ⋊ C31×Dic19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C31 | D57 |
| commutator, hypocenter | C3×C19 | C4×C31 |
| Frattini | C2 | C31×D57 |
| Fitting, socle | C2×C3×C19×C31 | C2 |
| LCS | G ▷ C3×C19 | |
| UCS | C1 ◁ C2×C31 | |
24 conjugacy classes of subgroups.
1860 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7068, 11);