Finite Group DatabasebetaFinite Group Databasebeta| order | 12012 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | D13⋊C3×D77 |
| unambiguous semidirect product | D13⋊(C3×D77) |
| unambiguous semidirect product | (C7×D13⋊C3)⋊D11 |
| unambiguous semidirect product | (C11×D13⋊C3)⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C11×C13 | C22×C3 |
| LCS | G ▷ C7×C11×C13 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
320 conjugacy classes — view the full character table.
| maximal subgroup of | D13⋊C3×C11⋊AGL(1,𝔽7), C3×D13⋊C3×D77, D13⋊C3×D231, … |
| maximal normal subgroup of | D13⋊C3×C11⋊AGL(1,𝔽7), C3×D13⋊C3×D77 |
| maximal quotient of | D77×D13⋊C9, C3×D13⋊C3×D77, D13⋊C3×D231, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12012, 89);