Finite Group DatabasebetaFinite Group Databasebeta| order | 2520 |
| isoclinism | isoclinic class of AΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5 · Schur multiplier (H2) = C3 |
| direct product | C3×C5×AΓL(1,𝔽8) |
| Fitting, socle | C23×C3×C5 ⋊ ΓL(1,𝔽8) |
| derived, Hall | AGL(1,𝔽8) ⋊ C32×C5 |
| Hall | C5×AGL(1,𝔽8) ⋊ C32 |
| Hall | C23×C5 ⋊ C3×ΓL(1,𝔽8) |
| Sylow | C23 ⋊ C3×C5×ΓL(1,𝔽8) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | AΓL(1,𝔽8) |
| commutator, cosocle, hypocenter | AGL(1,𝔽8) | C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C23×C3×C5 | ΓL(1,𝔽8) |
| LCS | G ▷ AGL(1,𝔽8) | |
| UCS | C1 ◁ C3×C5 | |
72 conjugacy classes of subgroups.
120 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×C5×AΓL(1,𝔽8) |
| maximal normal subgroup of | C2×C3×C5×AΓL(1,𝔽8) |
| maximal quotient of | C2×C3×C5×AΓL(1,𝔽8) |
Past the SmallGroups library coverage — no SmallGroups id.