Finite Group DatabasebetaFinite Group Databasebeta| order | 8190 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C13⋊C3×D105 |
| unambiguous semidirect product | C3⋊(C13⋊C3×D35) |
| unambiguous semidirect product | C5⋊(C13⋊C3×D21) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C7×C13 | C2×C3 |
| LCS | G ▷ C3×C5×C7×C13 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
378 conjugacy classes — view the full character table.
| maximal subgroup of | D13⋊C3×D105, ((C13⋊C3)⋊D7)⋊D15, D7×D15×C13⋊C3, … |
| maximal normal subgroup of | D13⋊C3×D105, ((C13⋊C3)⋊D7)⋊D15, D7×D15×C13⋊C3, … |
| maximal quotient of | C13⋊C3×Dic105, C2×C13⋊C3×D105 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8190, 117);