Finite Group DatabasebetaFinite Group Databasebeta| order | 12090 |
| isoclinism | isoclinic class of D155 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1 |
| direct product | C3×C13×D155 |
| unambiguous semidirect product | C5⋊(C3×C13×D31) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C13 | D155 |
| commutator, cosocle, hypocenter | C5×C31 | C2×C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C13×C31 | C2 |
| LCS | G ▷ C5×C31 | |
| UCS | C1 ◁ C3×C13 | |
32 conjugacy classes of subgroups.
3081 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D5×C13×D31, C3×D13×D155, C3×D65⋊D31, … |
| maximal normal subgroup of | C3×D5×C13×D31, C3×D13×D155, C3×D65⋊D31, … |
| maximal quotient of | C3×C13×Dic155, C2×C3×C13×D155, C9×C13×D155, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12090, 15);