Finite Group DatabasebetaFinite Group Databasebeta| order | 5832 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×#72221867 |
| Fitting | C2×C3×3−1+4 ⋊ C22 |
| derived | C3×#737 ⋊ C23×C3 |
| Sylow | C3×3−1+4 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #72221867 |
| commutator, cosocle, hypocenter | C3×#737 | C23×C3 |
| Frattini | C3 | C2×C3×C3⋊#1113 |
| Fitting | C2×C3×3−1+4 | C22 |
| socle | C2×C32 | C3×#1113 |
| LCS | G ▷ C3×#737 | |
| UCS | C1 ◁ C2 | |
3225 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
204 conjugacy classes — view the full character table.
| maximal quotient of | C2×#72221868 |
Past the SmallGroups library coverage — no SmallGroups id.