Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| unambiguous semidirect product | D5⋊#948 |
| Hall | C3×C5 ⋊ C2×#131 |
| Sylow | C5 ⋊ C2×#948 |
| Sylow | C3 ⋊ D5⋊#131 |
532 conjugacy classes of subgroups; only the 225 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 225 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^6,3,5|a^2=e,c^2=f,e^2=f,g^a=g^2,h^a=h^3,d^b=df,h^e=h^490 conjugacy classes — view the full character table.
| maximal subgroup of | #14295922, #14295978, #14296017, … |
| maximal normal subgroup of | #14295922, #14295978, #14296017, … |
| maximal quotient of | #14411316, C4×#91990, C4×#91992, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 11187);