Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Hall | C3×C5 ⋊ #486 |
| Sylow | C5 ⋊ #5070 |
| Sylow | C3 ⋊ #65049 |
236 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 236 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=e,b^2=e,d^2=f,b^a=be,c^a=ce,h^a=h^4,c^b=cd,d^b=df,g^b=g^2,d^c=df84 conjugacy classes — view the full character table.
| maximal subgroup of | #14437648, D3×#65049, C2×#11749102, … |
| maximal normal subgroup of | #14437648, D3×#65049, C2×#11749102, … |
| maximal quotient of | #14298823, #14304590, #14304592, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3297);