Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of D3×AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×Dic3×#170 |
| derived, Hall | C3×C5 ⋊ C2×C4×C8 |
| Sylow | C5 ⋊ C2×C8×Dic3 |
| Sylow | C3 ⋊ C2×C4×#170 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D3×AGL(1,𝔽5) |
| commutator, hypocenter | C3×C5 | C2×C4×C8 |
| Frattini | C22 | C2×D3×AGL(1,𝔽5) |
| Fitting, socle, prime radical | C23×C3×C5 | C2×C4 |
| cosocle | C2×C3×Dic5 | C23 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C23 | |
324 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 162 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 960 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | C4×Dic3×#170, Dic3×#4002, #14294264, … |
| maximal normal subgroup of | C4×Dic3×#170, Dic3×#4002, #14294264, … |
| maximal quotient of | C2×C3⋊C8×#170, C2×#11746485, #170×#208, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6180);