Finite Group DatabasebetaFinite Group Databasebeta| order | 15810 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D17×C31⋊C3 |
| unambiguous semidirect product | C17⋊(C2×C5×C31⋊C3) |
| unambiguous semidirect product | (C5×C31×D17)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D17×C31⋊C3 |
| commutator, cosocle, hypocenter | C17×C31 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C17×C31 | C2×C3 |
| LCS | G ▷ C17×C31 | |
| UCS | C1 ◁ C5 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2635 |
650 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×(C31⋊C3)⋊#595, C5×#595×C31⋊C3, C5×D17×D31⋊C3, … |
| maximal normal subgroup of | C5×(C31⋊C3)⋊#595, C5×#595×C31⋊C3, C5×D17×D31⋊C3, … |
| maximal quotient of | C5×Dic17×C31⋊C3, C2×C5×D17×C31⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15810, 28);