Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | D3×#43001 |
| Fitting | C3×#43001 ⋊ C2 |
| Sylow | C3 ⋊ C2×#43001 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C25×D3 |
| commutator, socle, cosocle | C23×C3 | C26 |
| Fitting | C3×#43001 | C2 |
| hypercenter | #43001 | D3 |
| hypocenter | C3 | C2×#43001 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ #43001 | |
At least 7130 conjugacy classes of subgroups; only the 4065 normal subgroups are shown.
174 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#7849701, D3×#7792761, D3×#7684106 |
| maximal normal subgroup of | D3×#7849701, D3×#7792761, D3×#7684106 |
| maximal quotient of | D3×#772778, D3×#1082737, D3×#1259281, … |
Past the SmallGroups library coverage — no SmallGroups id.