Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C4 · Schur multiplier (H2) = C29×C4 |
| direct product | C3×#581603 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C3 | C25 |
| commutator | C23 | C24×C3×C4 |
| Frattini, cosocle | C24 | C25×C3 |
| prime radical | C22×C3×#535 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C3 ◁ G | |
12292 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
312 conjugacy classes. The character table is too large to display.
| Fitting subgroup of | D3×#581603, #72253520, #72253676, … |
| maximal subgroup of | C3×#72210462, D3×#581603, #72253520, … |
| maximal normal subgroup of | C3×#72210462, D3×#581603, #72253520, … |
Past the SmallGroups library coverage — no SmallGroups id.