Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C5 ⋊ #328 |
| Sylow | C5 ⋊ #4452 |
| Sylow | C3 ⋊ #64869 |
160 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 42 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=c,b^2=e,d^2=f,b^a=bd,d^a=de,h^a=h^2,c^b=cef,d^b=df,g^b=g^2,h^c=h^457 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#64869, C2×#11746503, #14282743, … |
| maximal normal subgroup of | D3×#64869, C2×#11746503, #14282743, … |
| maximal quotient of | #14276670, #14276688, #14277147, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 698);