Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ #504 |
| Sylow | C5 ⋊ #4907 |
| Sylow | C3 ⋊ #65196 |
168 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 168 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.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^6,3,5|c^2=d,d^2=e,e^2=f,b^a=bf,c^a=cf,h^a=h^4,c^b=cf,g^b=g^2132 conjugacy classes — view the full character table.
| maximal subgroup of | #14478127, D5×#4907, D3×#65196, … |
| maximal normal subgroup of | #14478127, D5×#4907, D3×#65196, … |
| maximal quotient of | #14312671, #14312673, #14312675, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 1008);