Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #66161⋊C3 |
| Hall | #66161 ⋊ C3 |
| Sylow | C5 ⋊ #520⋊C3 |
168 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 45 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=h,e^2=h,f^2=h,b^a=bh,g^a=g^4,e^c=f,f^c=efh,f^e=fh94 conjugacy classes — view the full character table.
| maximal subgroup of | #14511827, #14511828, #14511829, … |
| maximal normal subgroup of | #14511827, #14511828, #14511829, … |
| maximal quotient of | SL(2,𝔽3)×C4⋊Dic5, #10614181⋊C3, #10614251⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6394);