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 ⋊ #410 |
| Sylow | C5 ⋊ #5240 |
| Sylow | C3 ⋊ #65295 |
316 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 104 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|b^2=d,c^2=f,b^a=be,d^a=df,h^a=h^4,e^b=ef,g^b=g^2114 conjugacy classes — view the full character table.
| maximal subgroup of | #14295524, #14295534, #14295537, … |
| maximal normal subgroup of | #14295524, #14295534, #14295537, … |
| maximal quotient of | #14280825, #14280911, #14280942, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 2819);