Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #5402 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #91902 |
| commutator, cosocle | C4×C5×A4 | C22 |
| Frattini, hypercenter | C4 | D5×S4 |
| Fitting | C22×C4×C5 | C2×D3 |
| socle | C23×C5 | D12 |
| hypocenter | C5×A4 | D8 |
| LCS | G ▷ C4×C5×A4 ▷ C2×C5×A4 ▷ C5×A4 | |
| UCS | C1 ◁ C2 ◁ C4 | |
158 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 25 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^4,3,5,2^2|a^2=c,c^2=d,b^a=bc,f^a=f^4,c^b=cd,e^b=e^2,g^b=h,h^b=g,g^e=h,h^e=gh50 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#5402, #14512911, #14512912, … |
| maximal normal subgroup of | D5×#5402, #14512911, #14512912, … |
| maximal quotient of | #14511672, #14511678, #14511680, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5770);