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 ⋊ #361 |
| Sylow | C5 ⋊ #4563 |
| Sylow | C3 ⋊ #64906 |
124 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 37 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,c^2=f,d^2=e,e^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^2,h^a=h^3,c^b=cf,d^b=def,e^b=ef,h^c=h^451 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11746777, D5⋊#4563, D3×#64906, … |
| maximal normal subgroup of | C2×#11746777, D5⋊#4563, D3×#64906, … |
| maximal quotient of | #14277851, #14277853, #14278219, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 972);