Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Hall | C3×C5 ⋊ C4×C4⋊C4 |
| Sylow | C5 ⋊ Dic3×C4⋊C4 |
| Sylow | C3 ⋊ #64938 |
388 conjugacy classes of subgroups.
| transitive degree | μt(G) = 960 |
Polycyclic presentation:
2^6,3,5|a^2=f,b^2=d,c^2=e,c^a=cf,h^a=h^4,c^b=cf,g^b=g^2132 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#64938, D5×Dic3×C4⋊C4, C4×#91404, … |
| maximal normal subgroup of | D3×#64938, D5×Dic3×C4⋊C4, C4×#91404, … |
| maximal quotient of | #14279849, #14279899, #14279934, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 2832);