Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C3×C5×C4⋊C4 ⋊ C22 |
| Hall | C3×C5 ⋊ #418 |
| Sylow | C5 ⋊ #4770 |
| Sylow | C3 ⋊ #65290 |
380 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 86 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=d,e^2=f,c^a=ce,e^a=ef,h^a=h^4,c^b=cf,g^b=g^2,e^c=ef96 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#4770, #14412389, D3×#65290, … |
| maximal normal subgroup of | D5×#4770, #14412389, D3×#65290, … |
| maximal quotient of | #14281700, #14281998, #14282296, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 1672);