Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of D5×C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C3 |
| direct product | D5×C3⋊(C3⋊C8) |
| derived, Hall | C32×C5 ⋊ C2×C8 |
| Sylow | C32 ⋊ C8×D5 |
| Sylow | C5 ⋊ C2×C3⋊(C3⋊C8) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D5×C3⋊D3 |
| commutator, hypocenter | C32×C5 | C2×C8 |
| Fitting, cosocle | C32×C4×C5 | C22 |
| socle | C2×C32×C5 | C2×C4 |
| prime radical | C2×C32×D5 | C4 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C4 | |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×C3⋊(C3⋊C8), #13085412, #13085413, … |
| maximal normal subgroup of | AGL(1,𝔽5)×C3⋊(C3⋊C8), #13085412, #13085413, … |
| maximal quotient of | D5×C3⋊(C3⋊C16), #13084702, Dic5×C3⋊(C3⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 220);