Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C5 ⋊ #479 |
| Sylow | C5 ⋊ #4799 |
| Sylow | C3 ⋊ #65118 |
180 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 960 |
Polycyclic presentation:
2^6,3,5|a^2=f,b^2=e,c^2=def,d^2=f,c^a=cd,d^a=df,h^a=h^4,c^b=cef,g^b=g^2105 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#65118, D5×#4799, C2×#11747864, … |
| maximal normal subgroup of | D3×#65118, D5×#4799, C2×#11747864, … |
| maximal quotient of | #14297791, #14300051, #14300187, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 2059);