Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of C3⋊((C24⋊C5)⋊C2) |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C3⋊#66245 |
| derived | C3×C24⋊C5 ⋊ C4 |
| Sylow | C3 ⋊ #66245 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊((C24⋊C5)⋊C2) |
| commutator, hypocenter | C3×C24⋊C5 | C4 |
| Fitting, socle | C25×C3 | D5 |
| prime radical, cosocle | C2×C3×C24⋊C5 | C2 |
| LCS | G ▷ C3×C24⋊C5 | |
| UCS | C1 ◁ C2 | |
222 conjugacy classes of subgroups.
| transitive degree | μt(G) = 60 |
Polycyclic presentation:
2^2,3,5,2^4|a^2=b,c^a=c^2,d^a=d^4,e^a=fg,g^a=ef,h^a=egh,e^d=f,f^d=fg,g^d=gh,h^d=eh36 conjugacy classes — view the full character table.
| maximal subgroup of | #14514349, Dic3×(C24⋊C5)⋊C2, D3×#66245, … |
| maximal normal subgroup of | #14514349, Dic3×(C24⋊C5)⋊C2, D3×#66245, … |
| maximal quotient of | C3⋊#10617015, C3⋊#10617016, C3⋊#10617017, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 11000);