Finite Group DatabasebetaFinite Group Databasebeta| order | 10062 |
| isoclinism | isoclinic class of D13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×D13⋊C9 |
| unambiguous semidirect product | D13⋊(C9×C43) |
| unambiguous semidirect product | (C13⋊C9)⋊(C2×C43) |
| derived, Sylow | C13 ⋊ C2×C9×C43 |
| Hall | C43×C13⋊C9 ⋊ C2 |
| Hall | D13×C43 ⋊ C9 |
| Hall | C13×C43 ⋊ C2×C9 |
| Hall | C13⋊C9 ⋊ C2×C43 |
| Hall | D13 ⋊ C9×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C43 | D13⋊C3 |
| commutator, hypocenter | C13 | C2×C9×C43 |
| Frattini | C3 | C43×D13⋊C3 |
| Fitting, socle | C3×C13×C43 | C2×C3 |
| prime radical | C3×D13×C43 | C3 |
| cosocle | C3×C13 | C2×C3×C43 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C3×C43 | |
24 conjugacy classes of subgroups.
1032 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C43×#261⋊C9, #34117428, D43×D13⋊C9, … |
| maximal normal subgroup of | C43×#261⋊C9, #34117428, D43×D13⋊C9, … |
| maximal quotient of | C43×Dic13⋊C9, C2×C43×D13⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10062, 18);