Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C24×C42 |
| direct product | C3×#72213396 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3 | #10745 |
| commutator | C22×Q8 | C2×C3×C42 |
| Frattini, cosocle | C23×#41 | C23×C3 |
| prime radical | C22×C3×#535 | C22 |
| LCS | G ▷ C22×Q8 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C23×C3×#41 ◁ G | |
7840 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
246 conjugacy classes — view the full character table.
| Fitting subgroup of | D3×#72213396 |
| maximal subgroup of | D3×#72213396 |
| maximal normal subgroup of | D3×#72213396 |
Past the SmallGroups library coverage — no SmallGroups id.