Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×C5×#100 ⋊ C2 |
| Hall | C3×C5 ⋊ #472 |
| Sylow | C5 ⋊ #4749 |
| Sylow | C3 ⋊ #65038 |
216 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^6,3,5|b^2=d,d^2=f,c^a=cde,e^a=ef,g^a=g^2,h^a=h^4,c^b=cef,e^b=ef,d^c=df93 conjugacy classes — view the full character table.
| maximal subgroup of | D15×#472, C2×#11750850, D5×#4749, … |
| maximal normal subgroup of | D15×#472, C2×#11750850, D5×#4749, … |
| maximal quotient of | #14291411, #14291450, #14291771, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5045);