Finite Group DatabasebetaFinite Group Databasebeta| order | 7030 |
| isoclinism | isoclinic class of D37 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C19 · Schur multiplier (H2) = C1 |
| direct product | C5×C19×D37 |
| unambiguous semidirect product | C37⋊(C2×C5×C19) |
| Fitting, socle, Hall | C5×C19×C37 ⋊ C2 |
| derived, Sylow | C37 ⋊ C2×C5×C19 |
| Hall | C19×C37 ⋊ C2×C5 |
| Hall | C5×C37 ⋊ C2×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C19 | D37 |
| commutator, hypocenter | C37 | C2×C5×C19 |
| Frattini | C1 | G |
| Fitting, socle | C5×C19×C37 | C2 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C5×C19 | |
16 conjugacy classes of subgroups.
1900 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C19×#3866, C5×C19⋊#3866, C5×D19×D37, … |
| maximal normal subgroup of | C5×C19×#3866, C5×C19⋊#3866, C5×D19×D37, … |
| maximal quotient of | C5×C19×Dic37, C2×C5×C19×D37, C3×C5×C19×D37, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7030, 2);