Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Hall | C3×C5 ⋊ #388 |
| Sylow | C5 ⋊ #4670 |
| Sylow | C3 ⋊ #64958 |
380 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 108 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=f,b^2=d,c^2=ef,c^a=cd,h^a=h^4,c^b=ce,g^b=g^2120 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#4670, D3×#64958, C2×#11748671, … |
| maximal normal subgroup of | D5×#4670, D3×#64958, C2×#11748671, … |
| maximal quotient of | #14279901, #14279983, #14280013, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 2866);