Finite Group DatabasebetaFinite Group Databasebeta| order | 6045 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #11925882⋊C5 |
| Fitting, socle, derived, Hall | C13×C31 ⋊ C3×C5 |
| Hall | C13×ΓL(1,𝔽32) ⋊ C3 |
| Hall | #11925882 ⋊ C5 |
| Hall | ΓL(1,𝔽32) ⋊ C13⋊C3 |
| Sylow | C31 ⋊ C5×C13⋊C3 |
| Sylow | C13 ⋊ (C31⋊C3)⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C31 | C3×C5 |
| LCS | G ▷ C13×C31 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
3,5,13,31|c^a=c^3,d^a=d^25,d^b=d^1661 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6045, 9);