Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #5428 |
138 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 23 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:
2^3,3,5,2^3|a^2=h,b^2=h,c^2=h,f^2=h,g^2=h,b^a=bc,c^a=ch,d^a=d^2,e^a=e^4,f^a=gh,g^a=fh,c^b=ch,f^d=g,g^d=fgh,g^f=gh55 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#5428, #14513573, #14513576, … |
| maximal normal subgroup of | D5×#5428, #14513573, #14513576, … |
| maximal quotient of | #14511989, #14511991, #14512003, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6342);