Finite Group DatabasebetaFinite Group Databasebeta| order | 5292 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | D3×ΓL(1,𝔽8)⋊AGL(1,𝔽7) |
| Fitting, socle, derived | C3×C72 ⋊ C22×C32 |
| Hall | C3×ΓL(1,𝔽8)2 ⋊ C22 |
| Sylow | C72 ⋊ C2×C32×D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C72 | C22×C32 |
| LCS | G ▷ C3×C72 | |
| UCS | C1 | |
348 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
78 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.