Finite Group DatabasebetaFinite Group Databasebeta| order | 10374 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×(C13⋊C3)⋊D19 |
| unambiguous semidirect product | (C13⋊C3)⋊(C7×D19) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | (C13⋊C3)⋊D19 |
| commutator, cosocle, hypocenter | C13×C19 | C2×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C13×C19 | C2×C3 |
| LCS | G ▷ C13×C19 | |
| UCS | C1 ◁ C7 | |
32 conjugacy classes of subgroups.
497 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10374, 57);