Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | C3×C5 ⋊ #342 |
| Sylow | C5 ⋊ #4527 |
| Sylow | C3 ⋊ #64747 |
284 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 92 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=cde,b^a=bd,d^a=df,h^a=h^4,c^b=cf,d^b=df,g^b=g^2114 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#4527, D3×#64747, #14294699, … |
| maximal normal subgroup of | D5×#4527, D3×#64747, #14294699, … |
| maximal quotient of | #14276825, #14276862, #14276865, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 215);