Finite Group DatabasebetaFinite Group Databasebeta| order | 12090 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C13⋊(D31⋊C5)) |
| unambiguous semidirect product | C13⋊(C3⋊(D31⋊C5)) |
| unambiguous semidirect product | ΓL(1,𝔽32)⋊D39 |
| unambiguous semidirect product | D1209⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C13×C31 | C2×C5 |
| LCS | G ▷ C3×C13×C31 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,13,31|b^a=b^2,d^a=d^12,e^a=e^30,e^c=e^16222 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12090, 32);