Finite Group DatabasebetaFinite Group Databasebeta| order | 12084 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| Fitting, socle, derived, Hall | C19×C53 ⋊ C22×C3 |
| Hall | D19×D53 ⋊ C3 |
| Hall | C53×C19⋊C3 ⋊ C22 |
| Hall | C19⋊C3 ⋊ C2×D53 |
| Sylow | C53 ⋊ C2×D19⋊C3 |
| Sylow | C19 ⋊ C2×C3×D53 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C19×C53 | C22×C3 |
| LCS | G ▷ C19×C53 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
252 conjugacy classes — view the full character table.
| maximal subgroup of | D53×AGL(1,𝔽19), C3×D53×D19⋊C3, D53×C3⋊(D19⋊C3), … |
| maximal normal subgroup of | D53×AGL(1,𝔽19), C3×D53×D19⋊C3 |
| maximal quotient of | D53×#4294⋊C2, C3×D53×D19⋊C3, D53×C3⋊(D19⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12084, 15);