Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×C42×C5 ⋊ C22 |
| Hall | C3×C5 ⋊ C2×#104 |
| Sylow | C5 ⋊ D3×#104 |
| Sylow | C3 ⋊ D5×#104 |
340 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 72 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|c^2=d,e^2=f,c^a=ce,d^a=df,e^a=ef,h^a=h^4,c^b=ce,d^b=df,e^b=ef,g^b=g^2102 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D5×#104, C2×#11747112, #14412857, … |
| maximal normal subgroup of | D3×D5×#104, C2×#11747112, #14412857, … |
| maximal quotient of | #14281499, #14281542, #14281593, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 1307);