Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×C5×#41 ⋊ C22 |
| Hall | C3×C5 ⋊ #577 |
| Sylow | C5 ⋊ #5770 |
| Sylow | C3 ⋊ #66109 |
516 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^6,3,5|c^2=f,d^2=f,e^2=f,d^a=de,e^a=ef,h^a=h^4,c^b=cf,d^b=de,e^b=ef,g^b=g^2,e^d=ef78 conjugacy classes — view the full character table.
| maximal subgroup of | #14457693, #14457707, #14457714, … |
| maximal normal subgroup of | #14457693, #14457707, #14457714, … |
| maximal quotient of | #14412668, #14412761, #14413476, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 9528);