Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #5912 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | D5×S4 |
| commutator, cosocle | C2×C5×A4 | C23 |
| Frattini | C2 | C2×D5×S4 |
| Fitting | C22×C4×C5 | C2×D3 |
| socle | C23×C5 | C22×D3 |
| hypocenter | C5×A4 | #41 |
| LCS | G ▷ C2×C5×A4 ▷ C5×A4 | |
| UCS | C1 ◁ C4 | |
342 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 41 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|c^2=d,b^a=bd,f^a=f^4,e^b=e^2,g^b=h,h^b=g,g^e=h,h^e=gh68 conjugacy classes — view the full character table.
| maximal subgroup of | #14512913, #14512914, #14512915, … |
| maximal normal subgroup of | #14512913, #14512914, #14512915, … |
| maximal quotient of | #14512634, #14512635, #14512643, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10947);