Finite Group DatabasebetaFinite Group Databasebeta| order | 27744 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | D3×#72213374 |
| Fitting, socle, derived, Hall | C3×C172 ⋊ C22×C8 |
| Sylow | C172 ⋊ C2×D3×C8 |
| Sylow | C3 ⋊ C2×#72213374 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C172 | C22×C8 |
| prime radical | D3×D172 | C4 |
| cosocle | C3×#11923883 | C23 |
| LCS | G ▷ C3×C172 | |
| UCS | C1 | |
480 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 102 |
120 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.