Finite Group DatabasebetaFinite Group Databasebeta| order | 11664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | D3×#14516829 |
| Sylow | C3×#6900 ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D3×#92265⋊C2 |
| commutator, cosocle | C2×C3×C92 | C23×C3 |
| Frattini | C2×C32 | C3×D33 |
| Fitting | C2×C3×#6900 | C23 |
| socle | C2×C33 | C2×C3×D32 |
| hypocenter | C3×C92 | C2×C3×D4 |
| LCS | G ▷ C2×C3×C92 ▷ C3×C92 | |
| UCS | C1 ◁ C2 | |
2129 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
189 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#72213202 |
| maximal normal subgroup of | D3×#72213202 |
Past the SmallGroups library coverage — no SmallGroups id.