Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of AGL(1,𝔽5)×S4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| derived | C5×A4 ⋊ C2×C8 |
| Sylow | C5 ⋊ C8×S4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | AGL(1,𝔽5)×S4 |
| commutator, hypocenter | C5×A4 | C2×C8 |
| Fitting, socle | C23×C5 | C4×D3 |
| prime radical | C2×C5⋊S4 | C4 |
| cosocle | A4×Dic5 | C22 |
| LCS | G ▷ C5×A4 | |
| UCS | C1 ◁ C2 | |
158 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^4,3,5,2^2|a^2=c,b^2=d,c^2=d,f^a=f^2,e^b=e^2,g^b=h,h^b=g,f^c=f^4,g^e=h,h^e=gh50 conjugacy classes — view the full character table.
| maximal subgroup of | S4×D5⋊C8, #14514279, #14514280, … |
| maximal normal subgroup of | S4×D5⋊C8, #14514279, #14514280, … |
| maximal quotient of | #14512350, #14512352, #14512373, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10903);