Finite Group DatabasebetaFinite Group Databasebeta| order | 10374 |
| isoclinism | isoclinic class of D57 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C13 · Schur multiplier (H2) = C1 |
| direct product | C7×C13×D57 |
| unambiguous semidirect product | C3⋊(C7×C13×D19) |
| unambiguous semidirect product | C19⋊(D3×C7×C13) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C13 | D57 |
| commutator, cosocle, hypocenter | C3×C19 | C2×C7×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C13×C19 | C2 |
| LCS | G ▷ C3×C19 | |
| UCS | C1 ◁ C7×C13 | |
32 conjugacy classes of subgroups.
2730 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C7×C13×D19, C7×D13×D57, C7×D39⋊D19, … |
| maximal normal subgroup of | D3×C7×C13×D19, C7×D13×D57, C7×D39⋊D19, … |
| maximal quotient of | C7×C13×Dic57, C2×C7×C13×D57, C7×C13×D171, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10374, 23);