Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C220 |
| direct product | D3×#7684106 |
| Fitting | C3×#7684106 ⋊ C2 |
| Sylow | C3 ⋊ C2×#7684106 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C26×D3 |
| commutator, socle, cosocle | C23×C3 | C27 |
| Fitting | C3×#7684106 | C2 |
| hypercenter | #7684106 | D3 |
| hypocenter | C3 | C2×#7684106 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ #7684106 | |
Only the 38141 normal subgroups are shown; non-normal subgroups are omitted.
339 conjugacy classes. The character table is too large to display.
| maximal quotient of | D3×#72214271 |
Past the SmallGroups library coverage — no SmallGroups id.