Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of D3×AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
| direct product | Dic3×#674 |
| derived, Hall | C3×C5 ⋊ C4×C16 |
| Sylow | C5 ⋊ Dic3×C16 |
| Sylow | C3 ⋊ C4×#674 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C4 | D3×AGL(1,𝔽5) |
| commutator, hypocenter | C3×C5 | C4×C16 |
| Fitting | C2×C3×C4×C5 | C2×C4 |
| socle, prime radical | C22×C3×C5 | C2×C8 |
| cosocle | C2×C3×#168 | C22 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C2×C4 | |
116 conjugacy classes of subgroups.
| transitive degree | μt(G) = 960 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D3×#674, C2×Dic3×#674, #14312537, … |
| maximal normal subgroup of | C4×D3×#674, C2×Dic3×#674, #14312537, … |
| maximal quotient of | C3⋊C8×#674, #14277481, #14278695, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 735);