Finite Group DatabasebetaFinite Group Databasebeta| order | 10374 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×D399 |
| unambiguous semidirect product | C3⋊(C13×D133) |
| unambiguous semidirect product | C7⋊(C13×D57) |
| unambiguous semidirect product | C19⋊(C13×D21) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D399 |
| commutator, cosocle, hypocenter | C3×C7×C19 | C2×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C13×C19 | C2 |
| LCS | G ▷ C3×C7×C19 | |
| UCS | C1 ◁ C13 | |
32 conjugacy classes of subgroups.
2613 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C13×D19×D21, D13×D399, D247⋊D21, … |
| maximal normal subgroup of | C13×D19×D21, D13×D399, D247⋊D21, … |
| maximal quotient of | C13×Dic399, C2×C13×D399, C13×D1197, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10374, 27);