Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of D5×A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C2 |
| direct product | Dic5×C22⋊C9 |
| unambiguous semidirect product | (C22×Dic5)⋊C9 |
| derived | C22×C5 ⋊ C4×C9 |
| Hall | C22×Dic5 ⋊ C9 |
| Sylow | C5 ⋊ C4×C22⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | D5×A4 |
| commutator, hypocenter | C22×C5 | C4×C9 |
| Fitting, socle, prime radical, cosocle | C23×C3×C5 | C2×C3 |
| LCS | G ▷ C22×C5 | |
| UCS | C1 ◁ C2×C3 | |
64 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 180 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | (C22⋊C9)⋊#170, C22⋊C9×#170, #13085154, … |
| maximal normal subgroup of | (C22⋊C9)⋊#170, C22⋊C9×#170, #13085154, … |
| maximal quotient of | C22⋊C9×#168, Dic5×Q8⋊C9, #4094⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 110);