Finite Group DatabasebetaFinite Group Databasebeta| order | 29040 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C26 |
| direct product | C2×D3×#11925892⋊C2 |
| Fitting, socle | C2×C3×C112 ⋊ C23×C5 |
| derived, Hall | C3×C112 ⋊ C24×C5 |
| Hall | C2×D3×D112 ⋊ C5 |
| Hall | C3×#10597243 ⋊ C24 |
| Hall | #10597243 ⋊ C23×D3 |
| Sylow | C112 ⋊ C23×C5×D3 |
| Sylow | C3 ⋊ C22×#11925892⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D3×#11925892⋊C2 |
| commutator, cosocle, hypocenter | C3×C112 | C24×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C112 | C23×C5 |
| LCS | G ▷ C3×C112 | |
| UCS | C1 ◁ C2 | |
1392 conjugacy classes of subgroups.
| transitive degree | μt(G) = 132 |
174 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#72213693 |
| maximal normal subgroup of | D3×#72213693 |
| maximal quotient of | D3×#72213693 |
Past the SmallGroups library coverage — no SmallGroups id.