Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C4 · Schur multiplier (H2) = C212 |
| direct product | C3×#517592 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C3 | C25 |
| commutator | C23 | C24×C3×C4 |
| Frattini, cosocle | C24 | C25×C3 |
| prime radical | C23×C3×H(5,𝔽2) | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C3 ◁ G | |
39772 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
384 conjugacy classes. The character table is too large to display.
| Fitting subgroup of | #72271489, D3×#517592 |
| maximal subgroup of | #72271489, D3×#517592, C3×#72214271 |
| maximal normal subgroup of | #72271489, D3×#517592, C3×#72214271 |
Past the SmallGroups library coverage — no SmallGroups id.