Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C211 |
| direct product | C3×#392113 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C3 | C22×C22⋊C4 |
| commutator | C24 | C23×C3×C4 |
| Frattini, cosocle | C23×C4 | C24×C3 |
| prime radical | C25×C3×D4 | C2 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C3 ◁ C25×C3×C4 ◁ G | |
57324 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
312 conjugacy classes. The character table is too large to display.
| Fitting subgroup of | D3×#392113, #72269885, #72271357, … |
| maximal subgroup of | C3×#72213256, D3×#392113, #72269885, … |
| maximal normal subgroup of | C3×#72213256, D3×#392113, #72269885, … |
Past the SmallGroups library coverage — no SmallGroups id.