Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Hall | C3×C5 ⋊ #427 |
| Sylow | C5 ⋊ #5106 |
| Sylow | C3 ⋊ #65169 |
228 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 96 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=d,c^2=ef,e^2=f,b^a=bf,h^a=h^4,c^b=ce,e^b=ef,g^b=g^2120 conjugacy classes — view the full character table.
| maximal subgroup of | #14278869, #14278870, #14278955, … |
| maximal normal subgroup of | #14278869, #14278870, #14278955, … |
| maximal quotient of | #14285570, #14285738, #14285930, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 1867);