Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of #6728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×#6728 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, socle, hypercenter | C2×C3 | S5 |
| commutator, cosocle, hypocenter | SL(2,𝔽5) | C2×C3 |
| Frattini | C2 | C3×S5 |
| prime radical | C3×SL(2,𝔽5) | C2 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C2×C3 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 144 |
36 conjugacy classes — view the full character table.
| maximal subgroup of | #13088289, #13088291, D3×#6728, … |
| maximal normal subgroup of | #13088289, #13088291, D3×#6728, … |
| maximal quotient of | C3×#91143, C2×C3×#6728 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 410);