Finite Group DatabasebetaFinite Group Databasebeta| order | 7980 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D665 |
| unambiguous semidirect product | (C5×D3)⋊D133 |
| unambiguous semidirect product | (D3×C7)⋊D95 |
| unambiguous semidirect product | (D3×C19)⋊D35 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C7×C19 | C22 |
| LCS | G ▷ C3×C5×C7×C19 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
1002 conjugacy classes — view the full character table.
| maximal subgroup of | D9×D665, D3×C5⋊#11716327, D3×C5⋊#11716328, … |
| maximal normal subgroup of | D3×C5⋊#11716327, D3×C5⋊#11716328, D3×C5⋊(ΓL(1,𝔽8)⋊D19), … |
| maximal quotient of | D9×D665, C3×D3×D665, D3×D1995, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7980, 159);