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 ⋊ #5022 |
| Sylow | C3 ⋊ #65311 |
180 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 75 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=e,b^2=ef,c^2=f,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^2,h^a=h^4,d^c=df159 conjugacy classes — view the full character table.
| maximal subgroup of | D15×#479, C2×#11751123, D5×#5022, … |
| maximal normal subgroup of | D15×#479, C2×#11751123, D5×#5022, … |
| maximal quotient of | #14297770, #14300010, #14300152, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5318);