Finite Group DatabasebetaFinite Group Databasebeta| order | 12090 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1 |
| direct product | D5×C13×C31⋊C3 |
| unambiguous semidirect product | C5⋊(C2×C13×C31⋊C3) |
| unambiguous semidirect product | (D5×C31)⋊(C3×C13) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D5×C31⋊C3 |
| commutator, cosocle, hypocenter | C5×C31 | C2×C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C5×C13×C31 | C2×C3 |
| LCS | G ▷ C5×C31 | |
| UCS | C1 ◁ C13 | |
32 conjugacy classes of subgroups.
676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12090, 45);