Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of ((C24⋊C5)⋊C2)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #66245⋊C3 |
| derived | C24⋊C5 ⋊ C3×C4 |
| Hall | #66245 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | ((C24⋊C5)⋊C2)⋊C3 |
| commutator, hypocenter | C24⋊C5 | C3×C4 |
| Fitting, socle | C25 | C3×D5 |
| prime radical | C2×AGL(1,𝔽16) | C2 |
| cosocle | C2×C24⋊C5 | C2×C3 |
| LCS | G ▷ C24⋊C5 | |
| UCS | C1 ◁ C2 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 60 |
Polycyclic presentation:
2,3,2,5,2^4|a^2=c,d^a=d^4,g^a=eg,h^a=efh,e^b=f,f^b=ef,g^b=egh,h^b=fg,e^d=h,f^d=fg,g^d=gh,h^d=efgh28 conjugacy classes — view the full character table.
| maximal subgroup of | #14514269, AGL(1,𝔽16)⋊Q8, C4×((C24⋊C5)⋊C2)⋊C3, … |
| maximal normal subgroup of | #14514269, AGL(1,𝔽16)⋊Q8, C4×((C24⋊C5)⋊C2)⋊C3, … |
| maximal quotient of | #10617015⋊C3, C2×#66245⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10893);