Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of ΓL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
No aliases for this group.
| derived, Hall | C3×C5 ⋊ C4×C16 |
| Sylow | C5 ⋊ C4×C3⋊C16 |
| Sylow | C3 ⋊ #64885 |
116 conjugacy classes of subgroups.
| transitive degree | μt(G) = 960 |
Polycyclic presentation:
2^6,3,5|a^2=c,b^2=de,c^2=e,e^2=f,g^a=g^2,h^a=h^3,h^c=h^4144 conjugacy classes — view the full character table.
| maximal subgroup of | C16×C3⋊#170, #170×C3⋊C16, #14277457, … |
| maximal normal subgroup of | C16×C3⋊#170, #170×C3⋊C16, #14277457, … |
| maximal quotient of | C8×C3⋊#674, #14277475, #14278689, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 951);