Finite Group DatabasebetaFinite Group Databasebeta| order | 6084 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #15690148⋊C2 |
| unambiguous semidirect product | #15690150⋊C2 |
| derived, Sylow | C132 ⋊ C22×C9 |
| Hall | #13095200 ⋊ C22 |
| Hall | D132 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #11759815⋊C2 |
| commutator, hypocenter | C132 | C22×C9 |
| Fitting, socle | C3×C132 | C22×C3 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C3 | |
96 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,13^2,3|c^3=f,e^a=e^12,d^b=d^12,d^c=d^3,e^c=e^396 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#15690148⋊C2, #15690150⋊D5, #15690148⋊D5 |
| maximal normal subgroup of | C5×#15690148⋊C2 |
| maximal quotient of | C5×#15690148⋊C2, #15690150⋊D5, #15690148⋊D5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6084, 86);