Finite Group DatabasebetaFinite Group Databasebeta| order | 12180 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D29×D105 |
| unambiguous semidirect product | (C3×D29)⋊D35 |
| unambiguous semidirect product | (C5×D29)⋊D21 |
| unambiguous semidirect product | (C7×D29)⋊D15 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C7×C29 | C22 |
| LCS | G ▷ C3×C5×C7×C29 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
864 conjugacy classes — view the full character table.
| maximal subgroup of | D29×D315, D29×C3⋊(C5⋊AGL(1,𝔽7)), C3×D29×D105, … |
| maximal normal subgroup of | D29×C3⋊(C5⋊AGL(1,𝔽7)), C3×D29×D105 |
| maximal quotient of | D29×D315, C3×D29×D105, D87⋊D105, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12180, 126);