Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ D4⋊C8 |
| Sylow | C5 ⋊ #4459 |
| Sylow | C3 ⋊ #64703 |
164 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 62 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|a^2=c,b^2=d,c^2=ef,d^2=f,b^a=bcd,h^a=h^4,c^b=ce,g^b=g^2132 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#64703, #14281490, C2×#11745839, … |
| maximal normal subgroup of | D3×#64703, #14281490, C2×#11745839, … |
| maximal quotient of | #14276647, #14276668, #14276802, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 34);