Finite Group DatabasebetaFinite Group Databasebeta| order | 15678 |
| isoclinism | isoclinic class of D13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C67 · Schur multiplier (H2) = C3 |
| direct product | C3×C67×D13⋊C3 |
| unambiguous semidirect product | D13⋊(C32×C67) |
| unambiguous semidirect product | (C13⋊C3)⋊(C2×C3×C67) |
| unambiguous semidirect product | (C3×D13)⋊(C3×C67) |
| Fitting, socle | C3×C13×C67 ⋊ C2×C3 |
| derived, Sylow | C13 ⋊ C2×C32×C67 |
| Hall | C3×C13⋊C3×C67 ⋊ C2 |
| Hall | D13×C67 ⋊ C32 |
| Hall | C13×C67 ⋊ C2×C32 |
| Hall | C3×C13⋊C3 ⋊ C2×C67 |
| Hall | D13 ⋊ C32×C67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C67 | D13⋊C3 |
| commutator, cosocle, hypocenter | C13 | C2×C32×C67 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C67 | C2×C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C3×C67 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2613 |
1608 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C67×AGL(1,𝔽13), C3×#23782989, C3×D13⋊C3×D67, … |
| maximal normal subgroup of | C3×C67×AGL(1,𝔽13), C3×#23782989, C3×D13⋊C3×D67, … |
| maximal quotient of | C3×C67×Dic13⋊C3, C2×C3×C67×D13⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15678, 31);