Finite Group DatabasebetaFinite Group Databasebeta| order | 15678 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#19104951 |
| Fitting, socle, derived | C3×C13×C67 ⋊ C2×C3 |
| Hall | C3×#14579732 ⋊ C2 |
| Hall | C13×C67 ⋊ C3×D3 |
| Sylow | C67 ⋊ C3⋊(D13⋊C3) |
| Sylow | C13 ⋊ C3⋊(D67⋊C3) |
| 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 |
Polycyclic presentation:
2,3^2,13,67|c^a=c^2,d^a=d^12,e^a=e^66,d^b=d^3,e^b=e^37444 conjugacy classes — view the full character table.
| maximal subgroup of | #19104943⋊D3, #19104947⋊D3, D3×#19104951, … |
| maximal normal subgroup of | #19104943⋊D3, #19104947⋊D3, D3×#19104951, … |
| maximal quotient of | C3⋊#23782981, C2×C3⋊#19104951 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15678, 46);