Finite Group DatabasebetaFinite Group Databasebeta| order | 12012 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×#10587716⋊C2 |
| unambiguous semidirect product | #10587716⋊(C2×C11) |
| unambiguous semidirect product | #10587720⋊(C2×C11) |
| unambiguous semidirect product | #10587722⋊(C2×C11) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | #10587716⋊C2 |
| commutator, cosocle, hypocenter | C7×C13 | C22×C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C7×C11×C13 | C22×C3 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C11 | |
80 conjugacy classes of subgroups.
264 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12012, 55);