Finite Group DatabasebetaFinite Group Databasebeta| order | 6480 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | AGL(1,𝔽5)×#4207⋊C2 |
| Fitting, derived, Hall | C5×#737 ⋊ C22×C4 |
| Sylow | #737 ⋊ C22×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C4×#4207⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C5×#737 | C22×C4 |
| Frattini | C3 | AGL(1,𝔽5)×#1113 |
| socle | C3×C5 | C4×#1113 |
| prime radical | D5×#4207⋊C2 | C2 |
| cosocle | D5×#737 | C23 |
| LCS | G ▷ C5×#737 | |
| UCS | C1 | |
718 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 718 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 135 |
105 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×(#4207⋊C2)⋊C3 |
| maximal normal subgroup of | AGL(1,𝔽5)×(#4207⋊C2)⋊C3 |
Past the SmallGroups library coverage — no SmallGroups id.