Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ #327 |
| Sylow | C5 ⋊ #4537 |
| Sylow | C3 ⋊ #64757 |
180 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 59 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,d^2=f,b^a=bd,d^a=def,g^a=g^2,h^a=h^4,c^b=ce,d^b=df117 conjugacy classes — view the full character table.
| maximal subgroup of | D15×#327, C2×#11746358, D5×#4537, … |
| maximal normal subgroup of | D15×#327, C2×#11746358, D5×#4537, … |
| maximal quotient of | #14276641, #14276656, #14277128, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 553);