Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29×C4 |
| direct product | D3×#15784 |
| Fitting | C3×#15784 ⋊ C2 |
| Sylow | C3 ⋊ C2×#15784 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C24×D3 |
| commutator, socle, cosocle | C24×C3 | C25 |
| Fitting | C3×#15784 | C2 |
| prime radical | C23×D3×D4 | C22 |
| hypercenter | #15784 | D3 |
| hypocenter | C3 | C2×#15784 |
| LCS | G ▷ C24×C3 ▷ C3 | |
| UCS | C1 ◁ C24 ◁ #15784 | |
13980 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
174 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#144415, D3×#4312024, D3×#1420724 |
| maximal normal subgroup of | D3×#144415, D3×#4312024, D3×#1420724 |
Past the SmallGroups library coverage — no SmallGroups id.