Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of Dic30 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#6705 |
| Fitting | C32×C5×C8 ⋊ C2 |
| Hall | C32×C5 ⋊ M16 |
| Sylow | C32 ⋊ #676 |
| Sylow | C5 ⋊ C3×ΓL(1,𝔽25) |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
198 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×ΓL(1,𝔽25), C3×D3×#676, C3×#91257, … |
| maximal normal subgroup of | C3×D5×ΓL(1,𝔽25), C3×D3×#676, C3×#91257, … |
| maximal quotient of | C3×#91098, C3×#91099, C3×#91104, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 336);