Finite Group DatabasebetaFinite Group Databasebeta| order | 29040 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | D3×#72213641 |
| derived, Hall | C3×C112 ⋊ C22×C4×C5 |
| Hall | D3×#11757244 ⋊ C5 |
| Hall | C3×#10597243 ⋊ C22×C4 |
| Hall | #10597243 ⋊ C2×C4×D3 |
| Sylow | C112 ⋊ C2×C4×C5×D3 |
| Sylow | C3 ⋊ C2×#72213641 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×#11925892⋊C2 |
| commutator, hypocenter | C3×C112 | C22×C4×C5 |
| Fitting, socle, cosocle | C2×C3×C112 | C23×C5 |
| prime radical | C2×D3×#11925892 | C2 |
| LCS | G ▷ C3×C112 | |
| UCS | C1 ◁ C2 | |
752 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 132 |
174 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#72213693 |
| maximal normal subgroup of | D3×#72213693 |
Past the SmallGroups library coverage — no SmallGroups id.