Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of D5×C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C3 |
| direct product | C22×D5×C3⋊D3 |
| Fitting, socle | C22×C32×C5 ⋊ C22 |
| derived, Hall | C32×C5 ⋊ C24 |
| Sylow | C32 ⋊ C23×D5 |
| Sylow | C5 ⋊ C23×C3⋊D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D5×C3⋊D3 |
| commutator, cosocle, hypocenter | C32×C5 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C22×C32×C5 | C22 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C22 | |
804 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#3722, #13085862, #13085863, … |
| maximal normal subgroup of | D5×#3722, #13085862, #13085863, … |
| maximal quotient of | C2×D5×#634, C2×#10624148, C2×#10624149, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 829);