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 ⋊ #436 |
| Sylow | C5 ⋊ #5128 |
| Sylow | C3 ⋊ #65018 |
244 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 76 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|c^2=d,d^2=f,b^a=bef,c^a=cf,h^a=h^4,c^b=ce,g^b=g^2120 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#65018, D5×#5128, C2×#11747723, … |
| maximal normal subgroup of | D3×#65018, D5×#5128, C2×#11747723, … |
| maximal quotient of | #14287270, #14287337, #14287372, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 1918);