Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C3 · Schur multiplier (H2) = C215 |
| direct product | C3×#10574840 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3 | C24×D4 |
| commutator, Frattini, cosocle | C2×C4 | C26×C3 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3 ◁ C23×C3×#41 ◁ G | |
46820 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
348 conjugacy classes. The character table is too large to display.
| Fitting subgroup of | #72271559, D3×#10574840 |
| maximal subgroup of | #72271559, C3×#72214173, D3×#10574840 |
| maximal normal subgroup of | #72271559, C3×#72214173, D3×#10574840 |
Past the SmallGroups library coverage — no SmallGroups id.