Finite Group DatabasebetaFinite Group Databasebeta| order | 10374 |
| isoclinism | isoclinic class of D39 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C19 · Schur multiplier (H2) = C1 |
| direct product | C7×C19×D39 |
| unambiguous semidirect product | C3⋊(C7×C19×D13) |
| unambiguous semidirect product | C13⋊(D3×C7×C19) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C19 | D39 |
| commutator, cosocle, hypocenter | C3×C13 | C2×C7×C19 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C13×C19 | C2 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C7×C19 | |
32 conjugacy classes of subgroups.
2793 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D19×D39, D3×C7×C19×D13, C7×D39⋊D19, … |
| maximal normal subgroup of | C7×D19×D39, D3×C7×C19×D13, C7×D39⋊D19, … |
| maximal quotient of | C7×C19×Dic39, C2×C7×C19×D39, C7×C19×D117, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10374, 24);