Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #65903⋊C3 |
| Hall | #65903 ⋊ C3 |
| Sylow | C5 ⋊ #557⋊C3 |
130 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 130 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^2,3,2^3,5,2|a^2=d,b^2=dh,e^2=h,f^2=h,b^a=bd,g^a=g^4,e^c=f,f^c=efh,f^e=fh91 conjugacy classes — view the full character table.
| maximal subgroup of | #14512605, #14512607, #14512609, … |
| maximal normal subgroup of | #14512605, #14512607, #14512609, … |
| maximal quotient of | SL(2,𝔽3)×#683, #10614192⋊C3, #10614191⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6353);