Finite Group DatabasebetaFinite Group Databasebeta| order | 6090 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(ΓL(1,𝔽8)⋊D29) |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊D145 |
| unambiguous semidirect product | C29⋊(C5⋊AGL(1,𝔽7)) |
| unambiguous semidirect product | D1015⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C7×C29 | C2×C3 |
| LCS | G ▷ C5×C7×C29 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,7,29|c^a=c^4,d^a=d^6,e^a=e^28,d^b=d^2367 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6090, 32);