Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×#13737⋊C3 |
| Fitting | C3×#13737 ⋊ C3 |
| Sylow | #13737 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C64 | A4 |
| commutator, hypocenter | Q8 | C32×C32 |
| Frattini | C32 | C2×C3×A4 |
| Fitting | C3×#13737 | C3 |
| socle | C2×C3 | A4×C32 |
| prime radical | C3×#41⋊C3 | C16 |
| cosocle | #2258 | C2×C32 |
| LCS | G ▷ Q8 | |
| UCS | C1 ◁ C3×C64 | |
112 conjugacy classes of subgroups.
672 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.