Finite Group DatabasebetaFinite Group Databasebeta| order | 6084 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C13 |
| direct product | D9×C13⋊D13 |
| unambiguous semidirect product | (C13×D9)⋊D13 |
| Fitting, derived, Hall | C9×C132 ⋊ C22 |
| Sylow | C132 ⋊ C2×D9 |
| Sylow | C9 ⋊ C2×C13⋊D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C9×C132 | C22 |
| Frattini | C3 | D3×C13⋊D13 |
| socle | C3×C132 | C2×D3 |
| LCS | G ▷ C9×C132 | |
| UCS | C1 | |
240 conjugacy classes of subgroups.
516 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D9×C13⋊D13, D45×C13⋊D13, D9×C5⋊(C13⋊D13), … |
| maximal normal subgroup of | C5×D9×C13⋊D13 |
| maximal quotient of | C5×D9×C13⋊D13, D45×C13⋊D13, D9×C5⋊(C13⋊D13), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6084, 111);