Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×C5×H(5,𝔽2) ⋊ C2 |
| Hall | C3×C5 ⋊ #577 |
| Sylow | C5 ⋊ #5836 |
| Sylow | C3 ⋊ #66170 |
516 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 163 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|b^2=f,c^2=f,d^2=f,e^2=f,d^a=de,e^a=ef,g^a=g^2,h^a=h^4,c^b=cf,e^d=ef141 conjugacy classes — view the full character table.
| maximal subgroup of | #14457662, #14457671, #14457714, … |
| maximal normal subgroup of | #14457662, #14457671, #14457714, … |
| maximal quotient of | #14412631, #14412709, #14413447, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10790);