Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Hall | C3×C5 ⋊ #564 |
| Sylow | C5 ⋊ C3⋊#564 |
| Sylow | C3 ⋊ C5⋊#564 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D3×D5 |
| commutator, socle, prime radical, cosocle | C22×C3×C5 | C24 |
| Fitting | C3×C5×C4⋊C4 | C22 |
| hypercenter | C4⋊C4 | D3×D5 |
| hypocenter | C3×C5 | #564 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
344 conjugacy classes of subgroups.
| transitive degree | μt(G) = 960 |
Polycyclic presentation:
2^6,3,5|a^2=f,b^2=e,c^2=ef,d^2=f,c^a=cf,d^a=de,h^a=h^4,c^b=cef,d^b=df,g^b=g^2,d^c=df81 conjugacy classes — view the full character table.
| maximal subgroup of | D5×C3⋊#564, D15⋊#564, D3×C5⋊#564, … |
| maximal normal subgroup of | D5×C3⋊#564, D15⋊#564, D3×C5⋊#564, … |
| maximal quotient of | #14331297, #14331298, #14331303, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 7528);