Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | Dic5×#41⋊C3 |
| unambiguous semidirect product | (#41×Dic5)⋊C3 |
| Hall | #41×Dic5 ⋊ C3 |
| Sylow | C5 ⋊ C4×#41⋊C3 |
180 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | Dic5×GU(2,𝔽3), #14511823, #14511824, … |
| maximal normal subgroup of | Dic5×GU(2,𝔽3), #14511823, #14511824, … |
| maximal quotient of | C4×Dic5×SL(2,𝔽3), #10614191⋊C3, #168×#41⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6392);