Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of D3×D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C43 |
| direct product | C4×Dic3×Dic5 |
| derived, Hall | C3×C5 ⋊ C43 |
| Sylow | C5 ⋊ C42×Dic3 |
| Sylow | C3 ⋊ C42×Dic5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | D3×D5 |
| commutator, hypocenter | C3×C5 | C43 |
| Frattini | C23 | C2×D3×D5 |
| Fitting | C22×C3×C4×C5 | C22 |
| socle, prime radical, cosocle | C23×C3×C5 | C23 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C22×C4 | |
516 conjugacy classes of subgroups; only the 264 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 264 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 960 |
192 conjugacy classes — view the full character table.
| maximal subgroup of | #14276743, C8×Dic3×Dic5, C4×Dic3×#170, … |
| maximal normal subgroup of | #14276743, C8×Dic3×Dic5, C4×Dic3×#170, … |
| maximal quotient of | Dic5×C3⋊#95, #14279849, Dic3×#3963, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 2829);