Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ #474 |
| Sylow | C5 ⋊ #4846 |
| Sylow | C3 ⋊ #65048 |
216 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^6,3,5|a^2=d,c^2=def,e^2=f,c^a=cd,h^a=h^4,c^b=ce,e^b=ef,g^b=g^299 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#4846, D3×#65048, C2×#11747765, … |
| maximal normal subgroup of | D5×#4846, D3×#65048, C2×#11747765, … |
| maximal quotient of | #14297658, #14299972, #14299978, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 1960);