Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C212×C4 |
| direct product | D3×#51068 |
| Fitting | C3×#51068 ⋊ C2 |
| Sylow | C3 ⋊ C2×#51068 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C25×D3 |
| commutator, socle, cosocle | C23×C3 | C26 |
| Fitting | C3×#51068 | C2 |
| hypercenter | #51068 | D3 |
| hypocenter | C3 | C2×#51068 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ #51068 | |
At least 6300 conjugacy classes of subgroups; only the 3683 normal subgroups are shown.
156 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#7792761 |
| maximal normal subgroup of | D3×#7792761 |
| maximal quotient of | D3×#1262353 |
Past the SmallGroups library coverage — no SmallGroups id.