Finite Group DatabasebetaFinite Group Databasebeta| order | 3240 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C9 |
| direct product | AGL(1,𝔽5)×C9⋊D9 |
| Fitting, derived, Hall | C5×C92 ⋊ C2×C4 |
| Sylow | C92 ⋊ C2×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C4×C9⋊D9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C5×C92 | C2×C4 |
| Frattini | C32 | C3⋊D3×AGL(1,𝔽5) |
| socle | C32×C5 | C4×C3⋊D3 |
| prime radical | D5×C9⋊D9 | C2 |
| cosocle | C92×D5 | C22 |
| LCS | G ▷ C5×C92 | |
| UCS | C1 | |
368 conjugacy classes of subgroups.
210 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#92314, D92×AGL(1,𝔽5) |
| maximal normal subgroup of | AGL(1,𝔽5)×#92314, D92×AGL(1,𝔽5) |
Past the SmallGroups library coverage — no SmallGroups id.