Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of D3×D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
| direct product | Dic5×C3⋊C16 |
| derived, Hall | C3×C5 ⋊ C4×C16 |
| Sylow | C5 ⋊ C4×C3⋊C16 |
| Sylow | C3 ⋊ C16×Dic5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C8 | D3×D5 |
| commutator, hypocenter | C3×C5 | C4×C16 |
| Fitting, cosocle | C2×C3×C5×C8 | C22 |
| socle, prime radical | C22×C3×C5 | C2×C8 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C2×C8 | |
116 conjugacy classes of subgroups.
| transitive degree | μt(G) = 960 |
192 conjugacy classes — view the full character table.
| maximal subgroup of | #170×C3⋊C16, #14277448, #14277463, … |
| maximal normal subgroup of | #170×C3⋊C16, #14277448, #14277463, … |
| maximal quotient of | #168×C3⋊C16, #14277479, #14278690, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 65);