Finite Group DatabasebetaFinite Group Databasebeta| order | 27744 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | D3×#72213346 |
| Fitting, socle, derived, Hall | C3×C172 ⋊ C2×C16 |
| Sylow | C172 ⋊ D3×C16 |
| Sylow | C3 ⋊ C2×#72213346 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C172 | C2×C16 |
| prime radical | D3×C17⋊D17 | C8 |
| cosocle | C3×#72213191 | C22 |
| LCS | G ▷ C3×C172 | |
| UCS | C1 | |
560 conjugacy classes of subgroups.
| transitive degree | μt(G) = 867 |
102 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#72213403 |
| maximal normal subgroup of | D3×#72213403 |
Past the SmallGroups library coverage — no SmallGroups id.