Finite Group DatabasebetaFinite Group Databasebeta| order | 10374 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D1729 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D1729 |
| commutator, cosocle, hypocenter | C7×C13×C19 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C13×C19 | C2 |
| LCS | G ▷ C7×C13×C19 | |
| UCS | C1 ◁ C3 | |
32 conjugacy classes of subgroups.
2598 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D19×D91, C3×D13×D133, C3×D7×D247, … |
| maximal normal subgroup of | C3×D19×D91, C3×D13×D133, C3×D7×D247, … |
| maximal quotient of | C3×Dic1729, C2×C3×D1729, C9×D1729, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10374, 21);