Finite Group DatabasebetaFinite Group Databasebeta| order | 10374 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×D273 |
| unambiguous semidirect product | C3⋊(C19×D91) |
| unambiguous semidirect product | C7⋊(C19×D39) |
| unambiguous semidirect product | C13⋊(C19×D21) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D273 |
| commutator, cosocle, hypocenter | C3×C7×C13 | C2×C19 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C13×C19 | C2 |
| LCS | G ▷ C3×C7×C13 | |
| UCS | C1 ◁ C19 | |
32 conjugacy classes of subgroups.
2622 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D19×D273, C19×D13×D21, D247⋊D21, … |
| maximal normal subgroup of | D19×D273, C19×D13×D21, D247⋊D21, … |
| maximal quotient of | C19×Dic273, C2×C19×D273, C19×D819, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10374, 28);