Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C27 |
| direct product | C3×#72219163 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3 | #10336 |
| commutator | C23×D4 | C22×C3×C4 |
| Frattini, cosocle | C24×D4 | C23×C3 |
| prime radical | C2×C3×#23897 | C2 |
| LCS | G ▷ C23×D4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3 ◁ C24×C3 ◁ C24×C3×D4 ◁ G | |
10294 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
228 conjugacy classes — view the full character table.
| Fitting subgroup of | #72270432, D3×#72219163 |
| maximal subgroup of | #72270432, D3×#72219163, C3×#72219167 |
| maximal normal subgroup of | #72270432, D3×#72219163, C3×#72219167 |
Past the SmallGroups library coverage — no SmallGroups id.