Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C5 ⋊ #358 |
| Sylow | C5 ⋊ #4492 |
| Sylow | C3 ⋊ #64723 |
116 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 116 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 960 |
Polycyclic presentation:
2^6,3,5|a^2=df,b^2=cde,c^2=ef,e^2=f,b^a=bc,c^a=ce,e^a=ef,h^a=h^4,g^b=g^2132 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#4492, #14313826, C2×#11745901, … |
| maximal normal subgroup of | D5×#4492, #14313826, C2×#11745901, … |
| maximal quotient of | #14277835, #14278203, #14278481, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 96);