Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Hall | C3×C5 ⋊ #542 |
| Sylow | C5 ⋊ #5561 |
| Sylow | C3 ⋊ #66067 |
432 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 128 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|b^2=e,c^2=e,d^2=ef,b^a=bf,d^a=def,h^a=h^4,c^b=ce,g^b=g^2,d^c=def90 conjugacy classes — view the full character table.
| maximal subgroup of | #14435654, #14435726, #14435780, … |
| maximal normal subgroup of | #14435654, #14435726, #14435780, … |
| maximal quotient of | #14322746, #14323221, #14323268, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 7560);