Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Hall | C3×C5 ⋊ #491 |
| Sylow | C5 ⋊ #5082 |
| Sylow | C3 ⋊ #65371 |
180 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 67 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=e,b^2=d,c^2=f,e^2=f,b^a=bf,c^a=cde,g^a=g^2,h^a=h^4,c^b=cd,e^c=ef114 conjugacy classes — view the full character table.
| maximal subgroup of | #14279513, #14279524, #14291141, … |
| maximal normal subgroup of | #14279513, #14279524, #14291141, … |
| maximal quotient of | #14298866, #14304639, #14305931, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5378);