Finite Group DatabasebetaFinite Group Databasebeta| order | 15990 |
| isoclinism | isoclinic class of D65 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C41 · Schur multiplier (H2) = C1 |
| direct product | C3×C41×D65 |
| unambiguous semidirect product | C5⋊(C3×D13×C41) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C41 | D65 |
| commutator, cosocle, hypocenter | C5×C13 | C2×C3×C41 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C13×C41 | C2 |
| LCS | G ▷ C5×C13 | |
| UCS | C1 ◁ C3×C41 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7995 |
4182 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C41×#63122, C3×#24922521, C3×C41×#63121, … |
| maximal normal subgroup of | C3×C41×#63122, C3×#24922521, C3×C41×#63121, … |
| maximal quotient of | C3×C41×Dic65, C2×C3×C41×D65 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15990, 10);