Finite Group DatabasebetaFinite Group Databasebeta| order | 15605 |
| automorphism | ? |
| homology | Abelianization (H1) = C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3121⋊C5 |
| Fitting, socle, derived, Sylow | C3121 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3121 | C5 |
| LCS | G ▷ C3121 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
5,3121|b^a=b^2163629 conjugacy classes — view the full character table.
| maximal subgroup of | D3121⋊C5, C2×C3121⋊C5 |
| maximal normal subgroup of | D3121⋊C5, C2×C3121⋊C5 |
| maximal quotient of | C2×C3121⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15605, 1);