Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of D5×C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C3×C4 |
| direct product | Dic5×C3⋊Dic3 |
| derived, Hall | C32×C5 ⋊ C42 |
| Sylow | C32 ⋊ C4×Dic5 |
| Sylow | C5 ⋊ C4×C3⋊Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | D5×C3⋊D3 |
| commutator, hypocenter | C32×C5 | C42 |
| Fitting, socle, prime radical, cosocle | C22×C32×C5 | C22 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C22 | |
180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 720 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊Dic3×#170, #13085433, #13085440, … |
| maximal normal subgroup of | C3⋊Dic3×#170, #13085433, #13085440, … |
| maximal quotient of | Dic5×C3⋊(C3⋊C8), C3⋊Dic3×#168, #13084719, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 238);