Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | C3×C5 ⋊ #413 |
| Sylow | C5 ⋊ #4751 |
| Sylow | C3 ⋊ #65526 |
300 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^6,3,5|a^2=d,c^2=f,d^2=f,c^a=ce,e^a=ef,h^a=h^4,c^b=cf,g^b=g^2,d^c=df93 conjugacy classes — view the full character table.
| maximal subgroup of | #14313642, #14313643, #14313648, … |
| maximal normal subgroup of | #14313642, #14313643, #14313648, … |
| maximal quotient of | #14280830, #14280877, #14281048, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3567);