Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C5 ⋊ #446 |
| Sylow | C5 ⋊ #5024 |
| Sylow | C3 ⋊ #65313 |
188 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 109 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=e,c^2=e,d^2=f,c^a=cf,g^a=g^2,h^a=h^4,c^b=ce168 conjugacy classes — view the full character table.
| maximal subgroup of | #14286598, #14286604, #14286638, … |
| maximal normal subgroup of | #14286598, #14286604, #14286638, … |
| maximal quotient of | #14296303, #14296369, #14303135, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5320);