Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×C3×C5×Q8 ⋊ C22 |
| Hall | C3×C5 ⋊ C2×#124 |
| Sylow | C5 ⋊ D3×#124 |
| Sylow | C3 ⋊ D5×#124 |
660 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 660 conjugacy classes of subgroups — too many to draw. Only its 144 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|c^2=f,d^2=f,c^a=cf,d^a=de,h^a=h^4,c^b=cf,d^b=de,g^b=g^2,d^c=df90 conjugacy classes — view the full character table.
| maximal subgroup of | #14283881, #14284071, #14284358, … |
| maximal normal subgroup of | #14283881, #14284071, #14284358, … |
| maximal quotient of | #14319996, #14320516, #14320784, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 9480);