Finite Group DatabasebetaFinite Group Databasebeta| order | 7030 |
| isoclinism | isoclinic class of D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C37 · Schur multiplier (H2) = C1 |
| direct product | C5×C37×D19 |
| unambiguous semidirect product | C19⋊(C2×C5×C37) |
| Fitting, socle, Hall | C5×C19×C37 ⋊ C2 |
| derived, Sylow | C19 ⋊ C2×C5×C37 |
| Hall | C19×C37 ⋊ C2×C5 |
| Hall | C5×C19 ⋊ C2×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C37 | D19 |
| commutator, hypocenter | C19 | C2×C5×C37 |
| Frattini | C1 | G |
| Fitting, socle | C5×C19×C37 | C2 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C5×C37 | |
16 conjugacy classes of subgroups.
2035 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D19×D37, D5×C37×D19, D19×D185, … |
| maximal normal subgroup of | C5×D19×D37, D5×C37×D19, D19×D185, … |
| maximal quotient of | C5×C37×Dic19, C2×C5×C37×D19, C3×C5×C37×D19, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7030, 3);