Finite Group DatabasebetaFinite Group Databasebeta| order | 3024 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2 |
| direct product | AGL(1,𝔽7)×AGL(1,𝔽9) |
| Fitting, socle, derived | C32×C7 ⋊ C2×C3×C8 |
| Hall | C32×ΓL(1,𝔽8) ⋊ C2×C8 |
| Sylow | C7 ⋊ C2×C3×AGL(1,𝔽9) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C7 | C2×C3×C8 |
| prime radical | C3⋊D3×AGL(1,𝔽7) | C4 |
| cosocle | C7×#157 | C22×C3 |
| LCS | G ▷ C32×C7 | |
| UCS | C1 | |
116 conjugacy classes of subgroups; only the 31 normal subgroups are shown.
This group has 116 conjugacy classes of subgroups — too many to draw. Only its 31 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
63 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.