Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Hall | C3×C5 ⋊ #490 |
| Sylow | C5 ⋊ #4764 |
| Sylow | C3 ⋊ #65360 |
220 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 60 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=e,b^2=d,e^2=f,b^a=bf,c^a=cde,h^a=h^4,c^b=cd,g^b=g^2,e^c=ef78 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#4764, #14437921, C2×#11748946, … |
| maximal normal subgroup of | D5×#4764, #14437921, C2×#11748946, … |
| maximal quotient of | #14298877, #14304735, #14304736, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3141);