Finite Group DatabasebetaFinite Group Databasebeta| order | 12012 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D7×D429 |
| unambiguous semidirect product | (C3×D7)⋊D143 |
| unambiguous semidirect product | (C11×D7)⋊D39 |
| unambiguous semidirect product | (C13×D7)⋊D33 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C7×C11×C13 | C22 |
| LCS | G ▷ C3×C7×C11×C13 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
1080 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7×D1287, #10587720⋊D33, #10587721⋊D33, … |
| maximal normal subgroup of | #10587720⋊D33, #10587721⋊D33, AGL(1,𝔽7)×D429, … |
| maximal quotient of | D7×D1287, C3×D7×D429, D21×D429, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12012, 154);