Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | C3×C5 ⋊ C4×D8 |
| Sylow | C5 ⋊ #4756 |
| Sylow | C3 ⋊ #65045 |
268 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 74 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|b^2=ef,c^2=de,d^2=f,c^a=cd,d^a=df,h^a=h^4,c^b=cd,d^b=df,g^b=g^2102 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#4756, D3×#65045, C4×#91256, … |
| maximal normal subgroup of | D5×#4756, D3×#65045, C4×#91256, … |
| maximal quotient of | #14286100, #14286537, #14286540, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 1928);