Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of D3×D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Hall | C32×C5 ⋊ C2×C8 |
| Sylow | C32 ⋊ C8×D5 |
| Sylow | C5 ⋊ #3710 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D3×D15 |
| commutator, hypocenter | C32×C5 | C2×C8 |
| Fitting, cosocle | C32×C4×C5 | C22 |
| socle | C2×C32×C5 | C2×C4 |
| prime radical | C2×C3⋊D15 | C4 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C4 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^4,3^2,5|a^2=c,b^2=c,c^2=d,f^a=f^2,g^a=g^4,e^b=e^2108 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#3710, D3×#6648, #13085643, … |
| maximal normal subgroup of | D5×#3710, D3×#6648, #13085643, … |
| maximal quotient of | #13084809, #13084812, #13084827, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 263);