Finite Group DatabasebetaFinite Group Databasebeta| order | 6140 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C307⋊AGL(1,𝔽5) |
| Fitting, socle, derived, Hall | C5×C307 ⋊ C4 |
| Sylow | C307 ⋊ AGL(1,𝔽5) |
| Sylow | C5 ⋊ Dic307 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C307 | C4 |
| LCS | G ▷ C5×C307 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5,307|a^2=b,c^a=c^2,d^a=d^306,c^b=c^4617 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6140, 7);