Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of D3×AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| direct product | D3×#3928 |
| derived, Hall | C3×C5 ⋊ C2×C32 |
| Sylow | C5 ⋊ D3×C32 |
| Sylow | C3 ⋊ C2×#3928 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | D3×AGL(1,𝔽5) |
| commutator, hypocenter | C3×C5 | C2×C32 |
| Fitting | C3×C5×C8 | C2×C4 |
| socle | C2×C3×C5 | C2×C16 |
| prime radical | C2×C5×D3 | C16 |
| cosocle | C3×#672 | C22 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C8 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 480 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#3928, D3×D5⋊C32, D3×#64877, … |
| maximal normal subgroup of | C2×D3×#3928, D3×D5⋊C32, D3×#64877, … |
| maximal quotient of | Dic3×#3928, (C2×D3)⋊#3928, Dic3⋊#3928, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 675);