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 ⋊ #4857 |
| Sylow | C3 ⋊ #65088 |
180 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 62 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=d,b^2=f,c^2=de,e^2=f,c^a=cde,e^a=ef,h^a=h^4,c^b=ce,e^b=ef,g^b=g^293 conjugacy classes — view the full character table.
| maximal subgroup of | #14430145, D3×#65088, C2×#11747885, … |
| maximal normal subgroup of | #14430145, D3×#65088, C2×#11747885, … |
| maximal quotient of | #14297794, #14300048, #14300184, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 2080);