Finite Group DatabasebetaFinite Group Databasebeta| order | 15690 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(D523⋊C3) |
| unambiguous semidirect product | (C523⋊C3)⋊D5 |
| unambiguous semidirect product | D2615⋊C3 |
| Fitting, socle, derived, Hall | C5×C523 ⋊ C2×C3 |
| Hall | C5×C523⋊C3 ⋊ C2 |
| Hall | D2615 ⋊ C3 |
| Hall | C523⋊C3 ⋊ D5 |
| Sylow | C523 ⋊ C3×D5 |
| Sylow | C5 ⋊ D523⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C523 | C2×C3 |
| LCS | G ▷ C5×C523 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2615 |
Polycyclic presentation:
2,3,5,523|c^a=c^4,d^a=d^522,d^b=d^462447 conjugacy classes — view the full character table.
| maximal subgroup of | D5×D523⋊C3, C2×C5⋊(D523⋊C3) |
| maximal normal subgroup of | D5×D523⋊C3, C2×C5⋊(D523⋊C3) |
| maximal quotient of | (C523⋊C3)⋊Dic5, C2×C5⋊(D523⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15690, 12);