Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
| direct product | C4×C3⋊#672 |
| derived, Hall | C3×C5 ⋊ C4×C16 |
| Sylow | C5 ⋊ C4×C3⋊C16 |
| Sylow | C3 ⋊ C4×#672 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C8 | D15 |
| commutator, hypocenter | C3×C5 | C4×C16 |
| Frattini | C2×C8 | C2×D15 |
| Fitting | C3×C4×C5×C8 | C2 |
| socle, prime radical | C22×C3×C5 | C2×C8 |
| cosocle | C2×C3×C5×C8 | C22 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C4×C8 | |
116 conjugacy classes of subgroups.
| transitive degree | μt(G) = 960 |
288 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×C3⋊#168, C8×C3⋊#672, #168×C3⋊C16, … |
| maximal normal subgroup of | C16×C3⋊#168, C8×C3⋊#672, #168×C3⋊C16, … |
| maximal quotient of | C8×C3⋊#672, #14277468, #14278683, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 476);