Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of D5×#157 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C3 |
| direct product | D5×#622 |
| derived, Hall | C32×C5 ⋊ C2×C8 |
| Sylow | C32 ⋊ C8×D5 |
| Sylow | C5 ⋊ C2×#622 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D5×#157 |
| commutator, hypocenter | C32×C5 | C2×C8 |
| Fitting, socle | C2×C32×C5 | C2×C4 |
| prime radical | C2×C32×D5 | C4 |
| cosocle | C5×C3⋊Dic3 | C22 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C2 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
48 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#622, #13088344, #13088365, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#622, #13088344, #13088365, … |
| maximal quotient of | D5×#3708, #13085516, Dic5×#622, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 456);