Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×ΓL(1,𝔽25) |
| Fitting | C32×C5×C8 ⋊ C2 |
| Hall | C32×C5 ⋊ M16 |
| Sylow | C32 ⋊ C5×M16 |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D5×ΓL(1,𝔽25), C3×#91246, C3×#91253, … |
| maximal normal subgroup of | C3×D5×ΓL(1,𝔽25), C3×#91246, C3×#91253, … |
| maximal quotient of | C3×C5×Dic3⋊C8, C3×C5×#815, C3×C5×(C2×D3)⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 320);