Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of C3⋊#66297 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C3⋊#66297 |
| Fitting, socle | C24×C3 ⋊ AGL(1,𝔽5) |
| derived | C3×C24⋊C5 ⋊ C4 |
| Sylow | C3 ⋊ #66297 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C3×C24⋊C5 | C4 |
| Fitting, socle | C24×C3 | AGL(1,𝔽5) |
| prime radical, cosocle | C3×(C24⋊C5)⋊C2 | C2 |
| LCS | G ▷ C3×C24⋊C5 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 30 |
Polycyclic presentation:
2^2,3,5,2^4|a^2=b,c^a=c^2,d^a=d^3,e^a=h,f^a=egh,g^a=eh,h^a=ef,d^b=d^4,e^b=ef,g^b=efh,h^b=eg,e^d=h,f^d=eh,g^d=efh,h^d=efgh21 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#66297, C2×C3⋊#66297, #72241553, … |
| maximal normal subgroup of | D3×#66297, C2×C3⋊#66297 |
| maximal quotient of | C3⋊#10619372, C3⋊#10619373, C3⋊#10619374, … |
| outer automorphism group of | #564 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 11363);