Finite Group DatabasebetaFinite Group Databasebeta| order | 15810 |
| isoclinism | isoclinic class of D31⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5×C17 · Schur multiplier (H2) = C1 |
| direct product | C3×C17×D31⋊C5 |
| unambiguous semidirect product | (C3×D31)⋊(C5×C17) |
| unambiguous semidirect product | (C3×C17×D31)⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C17 | D31⋊C5 |
| commutator, cosocle, hypocenter | C31 | C2×C3×C5×C17 |
| Frattini | C1 | G |
| Fitting, socle | C3×C17×C31 | C2×C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C3×C17 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1581 |
663 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D17×D31⋊C5, D3×C17×D31⋊C5, D51×D31⋊C5, … |
| maximal normal subgroup of | C3×D17×D31⋊C5, D3×C17×D31⋊C5, D51×D31⋊C5, … |
| maximal quotient of | C3×C17×Dic31⋊C5, C2×C3×C17×D31⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15810, 20);