Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C211 |
| direct product | C3×#72219165 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C3 | #2403 |
| commutator, Frattini, cosocle | C26 | C24×C3 |
| LCS | G ▷ C26 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C3 ◁ C26×C3 ◁ G | |
44266 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
282 conjugacy classes. The character table is too large to display.
| Fitting subgroup of | D3×#72219165 |
| maximal subgroup of | D3×#72219165 |
| maximal normal subgroup of | D3×#72219165 |
| maximal quotient of | C3×#72219167 |
Past the SmallGroups library coverage — no SmallGroups id.