Finite Group DatabasebetaFinite Group Databasebeta| order | 10374 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D741 |
| unambiguous semidirect product | C3⋊(C7×D247) |
| unambiguous semidirect product | C13⋊(C7×D57) |
| unambiguous semidirect product | C19⋊(C7×D39) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D741 |
| commutator, cosocle, hypocenter | C3×C13×C19 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C13×C19 | C2 |
| LCS | G ▷ C3×C13×C19 | |
| UCS | C1 ◁ C7 | |
32 conjugacy classes of subgroups.
2604 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D19×D39, C7×D13×D57, D3×C7×D247, … |
| maximal normal subgroup of | C7×D19×D39, C7×D13×D57, D3×C7×D247, … |
| maximal quotient of | C7×Dic741, C2×C7×D741, C7×D2223, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10374, 25);