Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | C3×C5 ⋊ #395 |
| Sylow | C5 ⋊ #4656 |
| Sylow | C3 ⋊ #64945 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C2×D3×D5 |
| commutator, socle, prime radical, cosocle | C23×C3×C5 | C23 |
| Fitting | C22×C3×C4×C5 | C22 |
| hypercenter | C22×C4 | D3×D5 |
| hypocenter | C3×C5 | #395 |
| LCS | G ▷ C23×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
364 conjugacy classes of subgroups.
| transitive degree | μt(G) = 960 |
Polycyclic presentation:
2^6,3,5|a^2=d,b^2=d,c^2=ef,b^a=bd,c^a=ce,h^a=h^4,c^b=cf,g^b=g^2114 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#4656, D3×#64945, #14331592, … |
| maximal normal subgroup of | D5×#4656, D3×#64945, #14331592, … |
| maximal quotient of | #14280151, #14280154, #14280157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3133);