Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ C2×SD32 |
| Sylow | C5 ⋊ D3×SD32 |
| Sylow | C3 ⋊ D5×SD32 |
180 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 46 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=f,b^2=f,d^2=ef,e^2=f,c^a=cd,d^a=de,e^a=ef,h^a=h^4,c^b=cd,d^b=de,e^b=ef,g^b=g^2,d^c=de,e^c=ef69 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D5×SD32, C2×#11748274, #14478279, … |
| maximal normal subgroup of | D3×D5×SD32, C2×#11748274, #14478279, … |
| maximal quotient of | #14313794, #14313823, #14314574, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 2469);