Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | AGL(1,𝔽5)×Dic12 |
| Hall | C3×C5 ⋊ C4×Q16 |
| Sylow | C5 ⋊ C4×Dic12 |
| Sylow | C3 ⋊ Q16×AGL(1,𝔽5) |
220 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
75 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#827, AGL(1,𝔽5)×#800, AGL(1,𝔽5)×#829, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#827, AGL(1,𝔽5)×#800, AGL(1,𝔽5)×#829, … |
| maximal quotient of | #14286270, #170×Dic12, #14286273, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5862);