Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C212 |
| direct product | C3×#772778 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C3 | C25 |
| commutator, Frattini, cosocle | C24 | C25×C3 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C3 ◁ G | |
23428 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
294 conjugacy classes. The character table is too large to display.
| Fitting subgroup of | D3×#772778, #72255403 |
| maximal subgroup of | D3×#772778, #72255403, C3×#72210469 |
| maximal normal subgroup of | D3×#772778, #72255403, C3×#72210469 |
Past the SmallGroups library coverage — no SmallGroups id.