Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Hall | C3×C5 ⋊ #576 |
| Sylow | C5 ⋊ #5835 |
| Sylow | C3 ⋊ #66169 |
536 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 152 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|e^2=f,b^a=be,e^a=ef,h^a=h^4,e^b=ef,g^b=g^2,d^c=df93 conjugacy classes — view the full character table.
| maximal subgroup of | #14457708, #14457710, #14457720, … |
| maximal normal subgroup of | #14457708, #14457710, #14457720, … |
| maximal quotient of | #14412685, #14412687, #14413537, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 9496);