Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C211 |
| direct product | C2×C3×D3×B(4,𝔽2) |
| Fitting | C2×C32×B(4,𝔽2) ⋊ C2 |
| Sylow | C32 ⋊ C22×B(4,𝔽2) |
14537 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
288 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×AGL(1,ℤ/9)×B(4,𝔽2), D3×AGL(1,𝔽7)×B(4,𝔽2) |
| maximal quotient of | C2×AGL(1,ℤ/9)×B(4,𝔽2), D3×AGL(1,𝔽7)×B(4,𝔽2) |
Past the SmallGroups library coverage — no SmallGroups id.