Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C2×AGL(1,𝔽5))⋊S4 |
| unambiguous semidirect product | (C2×S4)⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ (C2×S4)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | AGL(1,𝔽5)×S4 |
| commutator | C2×C5×A4 | C2×C4 |
| Fitting, socle | C23×C5 | C4×D3 |
| prime radical | C2×D5×S4 | C2 |
| cosocle | C2×D5×A4 | C22 |
| hypocenter | C5×A4 | C22⋊C4 |
| LCS | G ▷ C2×C5×A4 ▷ C5×A4 | |
| UCS | C1 ◁ C2 | |
286 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 60 |
Polycyclic presentation:
2^4,3,5,2^2|a^2=c,b^a=bd,f^a=f^2,e^b=e^2,g^b=h,h^b=g,f^c=f^4,g^e=h,h^e=gh38 conjugacy classes — view the full character table.
| maximal subgroup of | #14514284, #14514286, AGL(1,𝔽5)×C4⋊S4, … |
| maximal normal subgroup of | #14514284, #14514286, AGL(1,𝔽5)×C4⋊S4, … |
| maximal quotient of | #14512355, #14512356, #14512359, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10908);