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 ⋊ #441 |
| Sylow | C5 ⋊ #4853 |
| Sylow | C3 ⋊ #65005 |
216 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 216 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) = 960 |
Polycyclic presentation:
2^6,3,5|a^2=d,b^2=df,c^2=e,e^2=f,c^a=ce,e^a=ef,h^a=h^4,c^b=cf,g^b=g^2108 conjugacy classes — view the full character table.
| maximal subgroup of | #14315775, #14315787, #14315799, … |
| maximal normal subgroup of | #14315775, #14315787, #14315799, … |
| maximal quotient of | #14286413, #14287127, #14287599, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 2071);