Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(#401⋊C3) |
| unambiguous semidirect product | (C5⋊#401)⋊C3 |
| Hall | C5⋊#401 ⋊ C3 |
| Sylow | C5 ⋊ #401⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C5⋊(#126⋊C3) |
| commutator, Fitting, cosocle, hypocenter | C5×#95 | C2×C3 |
| Frattini | C23 | D5×A4 |
| socle | C23×C5 | C2×A4 |
| prime radical | C5×#95⋊C3 | C2 |
| LCS | G ▷ C5×#95 | |
| UCS | C1 ◁ C2 | |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2,3,2^2,5,2^3|a^2=h,c^2=g,d^2=f,c^a=cfg,d^a=dgh,e^a=e^4,c^b=cd,d^b=cfh,f^b=g,g^b=fgh,d^c=dh42 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C5⋊(#401⋊C3), #10605111⋊C3, #10605139⋊C3, … |
| maximal normal subgroup of | C2×C5⋊(#401⋊C3), #10605111⋊C3, #10605139⋊C3, … |
| maximal quotient of | #10600209⋊C3, C2×C5⋊(#401⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 797);