Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C28 |
| direct product | C3×#186814 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3 | C2×#379 |
| commutator | C22×C4 | C23×C3×C4 |
| Frattini, cosocle | C23×C4 | C24×C3 |
| prime radical | C3×#62811 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3 ◁ C24×C3×C4 ◁ G | |
7152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
222 conjugacy classes — view the full character table.
| Fitting subgroup of | #72271748, #72271761 |
| maximal subgroup of | C3×#72213489, #72271748, #72271761 |
| maximal normal subgroup of | C3×#72213489, #72271748, #72271761 |
Past the SmallGroups library coverage — no SmallGroups id.