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 ⋊ #430 |
| Sylow | C5 ⋊ #5124 |
| Sylow | C3 ⋊ #65729 |
204 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^6,3,5|a^2=d,b^2=e,c^2=f,d^2=f,e^2=f,b^a=be,e^a=ef,h^a=h^2,c^b=cf,g^b=g^2,h^d=h^460 conjugacy classes — view the full character table.
| maximal subgroup of | #14299700, #14299703, #14299704, … |
| maximal normal subgroup of | #14299700, #14299703, #14299704, … |
| maximal quotient of | #14285636, #14285637, #14285642, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5928);