Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Hall | C3×C5 ⋊ #405 |
| Sylow | C5 ⋊ #4689 |
| Sylow | C3 ⋊ #65728 |
260 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^6,3,5|a^2=d,c^2=e,d^2=f,e^2=f,h^a=h^2,c^b=cf,g^b=g^2,h^d=h^490 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#65728, C2×#11751671, #14411428, … |
| maximal normal subgroup of | D3×#65728, C2×#11751671, #14411428, … |
| maximal quotient of | #170×ΓL(1,𝔽25), #14280409, #14280473, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5866);