Finite Group DatabasebetaFinite Group Databasebeta| order | 1620 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | D5×#4176 |
| Fitting, Hall | C5×#731 ⋊ C22 |
| Sylow | #731 ⋊ C2×D5 |
| Sylow | C5 ⋊ C2×#4176 |
108 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 135 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#4176, D5×#4176⋊C2, #72268656, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#4176, D5×#4176⋊C2, #72268656, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1620, 113);