Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Hall | C3×C5 ⋊ B(4,𝔽2) |
| Sylow | C5 ⋊ #5244 |
| Sylow | C3 ⋊ #65321 |
396 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^6,3,5|b^a=bd,e^a=ef,h^a=h^4,c^b=ce,g^b=g^2,d^c=df81 conjugacy classes — view the full character table.
| maximal subgroup of | #14316648, #14316654, #14316660, … |
| maximal normal subgroup of | #14316648, #14316654, #14316660, … |
| maximal quotient of | #14287693, #14287699, #14287732, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3370);