Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C5 ⋊ #5389 |
112 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 27 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^3,3,5,2^3|a^2=c,b^2=ch,f^2=h,g^2=h,b^a=bc,d^a=d^2,e^a=e^4,f^a=gh,g^a=fh,f^d=g,g^d=fgh,g^f=gh79 conjugacy classes — view the full character table.
| maximal subgroup of | #14512603, #14512608, #14512613, … |
| maximal normal subgroup of | #14512603, #14512608, #14512613, … |
| maximal quotient of | #14511973, #14511977, #14511978, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6303);