Finite Group DatabasebetaFinite Group Databasebeta| order | 10374 |
| isoclinism | isoclinic class of D133 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1 |
| direct product | C3×C13×D133 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C13 | D133 |
| commutator, cosocle, hypocenter | C7×C19 | C2×C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C13×C19 | C2 |
| LCS | G ▷ C7×C19 | |
| UCS | C1 ◁ C3×C13 | |
32 conjugacy classes of subgroups.
2652 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C13×D7×D19, C3×D13×D133, C3×D91⋊D19, … |
| maximal normal subgroup of | C3×C13×D7×D19, C3×D13×D133, C3×D91⋊D19, … |
| maximal quotient of | C3×C13×Dic133, C2×C3×C13×D133, C9×C13×D133, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10374, 19);