Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22×C5×D4 ⋊ D3 |
| Sylow | C5 ⋊ #5415 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #91958 |
| commutator, cosocle | C4×C5×A4 | C22 |
| Frattini | C4 | C2×C5⋊S4 |
| Fitting | C22×C5×D4 | D3 |
| socle | C23×C5 | #67 |
| hypercenter | D4 | C5⋊S4 |
| hypocenter | C5×A4 | D8 |
| LCS | G ▷ C4×C5×A4 ▷ C2×C5×A4 ▷ C5×A4 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D4 | |
174 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 27 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=bc,c^a=cd,e^a=e^2,f^a=f^4,g^a=h,h^a=g,c^b=cd,g^e=h,h^e=gh59 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#5415, #14513177, #14513180, … |
| maximal normal subgroup of | D5×#5415, #14513177, #14513180, … |
| maximal quotient of | #14511964, #14511967, #14511999, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6329);