Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ #464 |
| Sylow | C5 ⋊ #4845 |
| Sylow | C3 ⋊ #65056 |
224 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^6,3,5|a^2=d,b^2=df,c^2=de,e^2=f,c^a=cdf,h^a=h^4,c^b=ce,e^b=ef,g^b=g^299 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#4845, #14426155, C2×#11747853, … |
| maximal normal subgroup of | D5×#4845, #14426155, C2×#11747853, … |
| maximal quotient of | #14291965, #14292091, #14292217, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 2048);