Finite Group DatabasebetaFinite Group Databasebeta| order | 15810 |
| isoclinism | isoclinic class of D51 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C31 · Schur multiplier (H2) = C1 |
| direct product | C5×C31×D51 |
| unambiguous semidirect product | C3⋊(C5×C31×D17) |
| unambiguous semidirect product | C17⋊(C5×D3×C31) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C31 | D51 |
| commutator, cosocle, hypocenter | C3×C17 | C2×C5×C31 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C17×C31 | C2 |
| LCS | G ▷ C3×C17 | |
| UCS | C1 ◁ C5×C31 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7905 |
4185 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D31×D51, C5×D3×C31×D17, C5×D51⋊D31, … |
| maximal normal subgroup of | C5×D31×D51, C5×D3×C31×D17, C5×D51⋊D31, … |
| maximal quotient of | C5×C31×Dic51, C2×C5×C31×D51 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15810, 14);