Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C3×C5×Q32 ⋊ C2 |
| Hall | C3×C5 ⋊ SD64 |
| Sylow | C5 ⋊ #4521 |
| Sylow | C3 ⋊ #64741 |
64 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^6,3,5|b^2=f,c^2=de,d^2=ef,e^2=f,b^a=bc,c^a=cd,d^a=de,e^a=ef,g^a=g^2,h^a=h^4,c^b=cd,d^b=de,e^b=ef96 conjugacy classes — view the full character table.
| maximal subgroup of | D15×SD64, C2×#11746342, D5×#4521, … |
| maximal normal subgroup of | D15×SD64, C2×#11746342, D5×#4521, … |
| maximal quotient of | #14279563, #14279585, #14279727, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 537);