Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ #444 |
| Sylow | C5 ⋊ #4823 |
| Sylow | C3 ⋊ #65741 |
208 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^6,3,5|a^2=d,b^2=f,c^2=f,d^2=f,e^2=f,c^a=ce,e^a=ef,h^a=h^2,c^b=cef,e^b=ef,g^b=g^2,e^c=ef,h^d=h^448 conjugacy classes — view the full character table.
| maximal subgroup of | #14417984, C2×#11751982, D3×#65741, … |
| maximal normal subgroup of | #14417984, C2×#11751982, D3×#65741, … |
| maximal quotient of | #14286356, #14286366, #14286417, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6177);