Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C5 ⋊ #499 |
| Sylow | C5 ⋊ #5065 |
| Sylow | C3 ⋊ #65147 |
172 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 66 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=e,c^2=d,e^2=f,c^a=cdf,h^a=h^4,c^b=cef,g^b=g^2,e^c=ef84 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#5065, D3×#65147, C2×#11747144, … |
| maximal normal subgroup of | D5×#5065, D3×#65147, C2×#11747144, … |
| maximal quotient of | #14299110, #14305056, #14305071, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 1339);