Finite Group DatabasebetaFinite Group Databasebeta| order | 15990 |
| isoclinism | isoclinic class of D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13×C41 · Schur multiplier (H2) = C1 |
| direct product | C13×D15×C41 |
| unambiguous semidirect product | C3⋊(D5×C13×C41) |
| unambiguous semidirect product | C5⋊(D3×C13×C41) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13×C41 | D15 |
| commutator, cosocle, hypocenter | C3×C5 | C2×C13×C41 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C13×C41 | C2 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C13×C41 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7995 |
4797 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C13×D15×D41, D13×D15×C41, D15×D533, … |
| maximal normal subgroup of | C13×D15×D41, D13×D15×C41, D15×D533, … |
| maximal quotient of | C13×C41×Dic15, C2×C13×D15×C41 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15990, 16);