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 | C3⋊D3×#168 |
| derived, Hall | C32×C5 ⋊ C2×C8 |
| Sylow | C32 ⋊ C2×#168 |
| Sylow | C5 ⋊ C8×C3⋊D3 |
| 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×C5×C3⋊D3 | 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 | C3⋊D3×#674, #13085429, #13085483, … |
| maximal normal subgroup of | C3⋊D3×#674, #13085429, #13085483, … |
| maximal quotient of | C3⋊D3×#672, #13084703, C3⋊Dic3×#168, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 221);