Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×C5×#106 ⋊ C2 |
| Hall | C3×C5 ⋊ C4×SD16 |
| Sylow | C5 ⋊ #4852 |
| Sylow | C3 ⋊ #65141 |
244 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 79 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|a^2=e,b^2=e,c^2=ef,d^2=f,g^a=g^2,h^a=h^4,c^b=cd,d^b=df,d^c=df126 conjugacy classes — view the full character table.
| maximal subgroup of | C4×SD16×D15, C2×#11750953, D5×#4852, … |
| maximal normal subgroup of | C4×SD16×D15, C2×#11750953, D5×#4852, … |
| maximal quotient of | #14286130, #14286592, #14286687, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5148);