Finite Group DatabasebetaFinite Group Databasebeta| order | 12090 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×D403 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | D403 |
| commutator, cosocle, hypocenter | C13×C31 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C13×C31 | C2 |
| LCS | G ▷ C13×C31 | |
| UCS | C1 ◁ C3×C5 | |
32 conjugacy classes of subgroups.
3045 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×D13×D31, C3×D5×D403, C3×D65⋊D31, … |
| maximal normal subgroup of | C3×C5×D13×D31, C3×D5×D403, C3×D65⋊D31, … |
| maximal quotient of | C3×C5×Dic403, C2×C3×C5×D403, C5×C9×D403, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12090, 13);