Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | C3×C5 ⋊ #450 |
| Sylow | C5 ⋊ #4731 |
| Sylow | C3 ⋊ #65335 |
376 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 376 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) = 240 |
Polycyclic presentation:
2^6,3,5|a^2=d,b^2=f,d^2=f,b^a=bdf,c^a=ce,h^a=h^4,c^b=ce,d^b=df,g^b=g^299 conjugacy classes — view the full character table.
| maximal subgroup of | #14287735, #14287741, #14287749, … |
| maximal normal subgroup of | #14287735, #14287741, #14287749, … |
| maximal quotient of | #14287982, #14288123, #14288546, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 2749);