Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ #339 |
| Sylow | C5 ⋊ #4532 |
| Sylow | C3 ⋊ #64775 |
220 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 92 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=c,b^2=d,d^2=f,e^2=f,b^a=be,e^a=ef,h^a=h^4,e^b=ef,g^b=g^2120 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#4532, #14294455, C2×#11745973, … |
| maximal normal subgroup of | D5×#4532, #14294455, C2×#11745973, … |
| maximal quotient of | #14276739, #14276779, #14276803, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 168);