Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of C22⋊AGL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊AGL(1,𝔽16) |
| unambiguous semidirect product | (C24⋊C5)⋊A4 |
| unambiguous semidirect product | (C22⋊(C22⋊A4))⋊C5 |
| Fitting, socle, derived, Sylow | C26 ⋊ C3×C5 |
| Hall | C22×C24⋊C5 ⋊ C3 |
| Hall | C22⋊(C22⋊A4) ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C26 | C3×C5 |
| LCS | G ▷ C26 | |
| UCS | C1 | |
221 conjugacy classes of subgroups.
| transitive degree | μt(G) = 20 |
Polycyclic presentation:
3,5,2^6|c^a=cd,d^a=c,e^a=cf,f^a=def,g^a=gh,h^a=g,c^b=de,d^b=def,e^b=c,f^b=ce24 conjugacy classes — view the full character table.
| derived subgroup of | #72240861 |
| maximal subgroup of | ((C24⋊C5)⋊C2)⋊A4, C2×C22⋊AGL(1,𝔽16) |
| maximal normal subgroup of | ((C24⋊C5)⋊C2)⋊A4, C2×C22⋊AGL(1,𝔽16) |
| maximal quotient of | Q8⋊AGL(1,𝔽16), C2×C22⋊AGL(1,𝔽16) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 11367);