Finite Group DatabasebetaFinite Group Databasebeta| order | 15678 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C13⋊C3×D201 |
| unambiguous semidirect product | C3⋊(C13⋊C3×D67) |
| Fitting, socle, derived | C3×C13×C67 ⋊ C2×C3 |
| Hall | C3×C13⋊C3×C67 ⋊ C2 |
| Hall | C13×C67 ⋊ C3×D3 |
| Hall | C3×C13⋊C3 ⋊ D67 |
| Sylow | C67 ⋊ D3×C13⋊C3 |
| Sylow | C13 ⋊ C3×D201 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C13×C67 | C2×C3 |
| LCS | G ▷ C3×C13×C67 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2613 |
714 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D13⋊C3×D201, (C3⋊(D13⋊C3))⋊D67, D3×C13⋊C3×D67, … |
| maximal normal subgroup of | D13⋊C3×D201, (C3⋊(D13⋊C3))⋊D67, D3×C13⋊C3×D67, … |
| maximal quotient of | C13⋊C3×Dic201, C2×C13⋊C3×D201 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15678, 55);