Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×C3×C5×D4 ⋊ C4 |
| Hall | C3×C5 ⋊ #353 |
| Sylow | C5 ⋊ #4545 |
| Sylow | C3 ⋊ #64922 |
172 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 33 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^6,3,5|a^2=c,d^2=f,b^a=bd,d^a=def,e^a=ef,g^a=g^2,h^a=h^3,c^b=ce,d^b=df,d^c=df,h^c=h^457 conjugacy classes — view the full character table.
| maximal subgroup of | #14279304, #14279306, #14279315, … |
| maximal normal subgroup of | #14279304, #14279306, #14279315, … |
| maximal quotient of | #14277583, #14277690, #14278081, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 988);