Finite Group DatabasebetaFinite Group Databasebeta| order | 12168 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | D3×#14523148 |
| Fitting, socle, derived | C3×C132 ⋊ C2×C3×C4 |
| Hall | C3×#92788 ⋊ C2×C4 |
| Sylow | C132 ⋊ C3×C4×D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C132 | C2×C3×C4 |
| prime radical | D3×#11759817 | C2 |
| cosocle | C3×C13×D13 | C22×C3 |
| LCS | G ▷ C3×C132 | |
| UCS | C1 | |
167 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 167 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 156 |
87 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#72214102 |
| maximal normal subgroup of | D3×#72214102 |
Past the SmallGroups library coverage — no SmallGroups id.