Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C3×C5×C8 ⋊ C4 |
| Hall | C3×C5 ⋊ #344 |
| Sylow | C5 ⋊ #4556 |
| Sylow | C3 ⋊ #64894 |
180 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 61 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|a^2=c,b^2=d,d^2=f,b^a=be,e^a=ef,g^a=g^2,h^a=h^3,c^b=cf,h^c=h^490 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11746765, #14294823, D3×#64894, … |
| maximal normal subgroup of | C2×#11746765, #14294823, D3×#64894, … |
| maximal quotient of | #14276839, #14276858, #14276885, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 960);