Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C5 ⋊ #334 |
| Sylow | C5 ⋊ #4480 |
| Sylow | C3 ⋊ #64700 |
108 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 960 |
Polycyclic presentation:
2^6,3,5|a^2=d,b^2=c,c^2=e,d^2=f,b^a=bdf,g^a=g^2,h^a=h^4,d^b=df168 conjugacy classes — view the full character table.
| maximal subgroup of | D15×#334, C2×#11746301, D5×#4480, … |
| maximal normal subgroup of | D15×#334, C2×#11746301, D5×#4480, … |
| maximal quotient of | #14276746, #14278571, #14278586, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 496);