Finite Group DatabasebetaFinite Group Databasebeta| order | 7992 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×#72228574 |
| Fitting, socle | C2×C3×C37 ⋊ C4×C9 |
| derived | C3×C37 ⋊ C2×C4×C9 |
| Hall | C3×#66526 ⋊ C2×C4 |
| Sylow | C37 ⋊ C2×C9×Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #72228574 |
| commutator, hypocenter | C3×C37 | C2×C4×C9 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C37 | C4×C9 |
| prime radical | C2×C3×D37⋊C3 | C2×C3 |
| cosocle | C3×D37⋊C3 | C22×C3 |
| LCS | G ▷ C3×C37 | |
| UCS | C1 ◁ C2 | |
116 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 116 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 222 |
114 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×AGL(1,𝔽37) |
| maximal normal subgroup of | C2×D3×AGL(1,𝔽37) |
Past the SmallGroups library coverage — no SmallGroups id.