Finite Group DatabasebetaFinite Group Databasebeta| order | 15678 |
| isoclinism | isoclinic class of D67⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C13 · Schur multiplier (H2) = C3 |
| direct product | C3×C13×D67⋊C3 |
| unambiguous semidirect product | D67⋊(C32×C13) |
| unambiguous semidirect product | (C67⋊C3)⋊(C2×C3×C13) |
| unambiguous semidirect product | (C3×D67)⋊(C3×C13) |
| Fitting, socle | C3×C13×C67 ⋊ C2×C3 |
| derived, Sylow | C67 ⋊ C2×C32×C13 |
| Hall | C3×C13×C67⋊C3 ⋊ C2 |
| Hall | C13×D67 ⋊ C32 |
| Hall | C13×C67 ⋊ C2×C32 |
| Hall | C3×C67⋊C3 ⋊ C2×C13 |
| Hall | D67 ⋊ C32×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C13 | D67⋊C3 |
| commutator, cosocle, hypocenter | C67 | C2×C32×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C67 | C2×C3 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C3×C13 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2613 |
663 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D13×D67⋊C3, D3×C13×D67⋊C3, D39×D67⋊C3, … |
| maximal normal subgroup of | C3×D13×D67⋊C3, D3×C13×D67⋊C3, D39×D67⋊C3, … |
| maximal quotient of | C3×C13×(C67⋊C3)⋊C4, C2×C3×C13×D67⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15678, 30);