Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C216 |
| direct product | D3×#846041 |
| Fitting | C3×#846041 ⋊ C2 |
| Sylow | C3 ⋊ C2×#846041 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C25×D3 |
| commutator, socle, cosocle | C24×C3 | C26 |
| Fitting | C3×#846041 | C2 |
| hypercenter | #846041 | D3 |
| hypocenter | C3 | C2×#846041 |
| LCS | G ▷ C24×C3 ▷ C3 | |
| UCS | C1 ◁ C24 ◁ #846041 | |
At least 18452 conjugacy classes of subgroups; only the 5863 normal subgroups are shown.
276 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×#72210469 |
| maximal normal subgroup of | D3×#72210469 |
| maximal quotient of | D3×#72215520 |
Past the SmallGroups library coverage — no SmallGroups id.