Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×C5×#123 ⋊ C2 |
| Hall | C3×C5 ⋊ #551 |
| Sylow | C5 ⋊ #5658 |
| Sylow | C3 ⋊ #65992 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D15 |
| commutator, socle, cosocle | C22×C3×C5 | C24 |
| Fitting | C3×C5×#123 | C2 |
| prime radical | #91826 | C2 |
| hypercenter | #123 | D15 |
| hypocenter | C3×C5 | #551 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ #123 | |
496 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^6,3,5|c^2=e,d^2=f,c^a=cf,g^a=g^2,h^a=h^4,d^b=de,d^c=df123 conjugacy classes — view the full character table.
| maximal subgroup of | D15×#551, C2×#11756417, D5×#5658, … |
| maximal normal subgroup of | D15×#551, C2×#11756417, D5×#5658, … |
| maximal quotient of | #14326220, #14326235, #14326397, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10612);