Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C16 · Schur multiplier (H2) = C4 |
| direct product | C4×C5×C3⋊C16 |
| derived, Sylow | C3 ⋊ C4×C5×C16 |
| Hall | C3×C5 ⋊ C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C5×C8 | D3 |
| commutator, hypocenter | C3 | C4×C5×C16 |
| Frattini | C2×C8 | C2×C5×D3 |
| Fitting | C3×C4×C5×C8 | C2 |
| socle, prime radical | C22×C3×C5 | C2×C8 |
| cosocle | C2×C3×C8 | C22×C5 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C4×C5×C8 | |
116 conjugacy classes of subgroups.
| transitive degree | μt(G) = 960 |
480 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C16×C3⋊C8, C5×C8×C3⋊C16, #168×C3⋊C16, … |
| maximal normal subgroup of | C5×C16×C3⋊C8, C5×C8×C3⋊C16, #168×C3⋊C16, … |
| maximal quotient of | C5×C8×C3⋊C16, C5×#67438, C5×#67657, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 354);