Finite Group DatabasebetaFinite Group Databasebeta| order | 6084 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C3⋊(D13⋊C3))⋊D13 |
| unambiguous semidirect product | ((C13⋊C3)⋊D13)⋊D3 |
| Fitting, socle, derived | C3×C132 ⋊ C22×C3 |
| Hall | C3×C13×C13⋊C3 ⋊ C22 |
| Sylow | C132 ⋊ C2×C3×D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C132 | C22×C3 |
| LCS | G ▷ C3×C132 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3^2,13^2|d^a=d^2,e^a=e^12,e^b=e^12,f^b=f^12,e^c=e^3114 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6084, 215);