Finite Group DatabasebetaFinite Group Databasebeta| order | 2688 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C211 |
| direct product | D3×D7×#120 |
| Fitting | C3×C7×#120 ⋊ C22 |
| Hall | C3×C7 ⋊ C22×#120 |
| Sylow | C7 ⋊ C2×D3×#120 |
| Sylow | C3 ⋊ C2×D7×#120 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D3×D7 |
| commutator, socle, cosocle | C22×C3×C7 | C25 |
| Fitting | C3×C7×#120 | C22 |
| hypercenter | #120 | D3×D7 |
| hypocenter | C3×C7 | C22×#120 |
| LCS | G ▷ C22×C3×C7 ▷ C3×C7 | |
| UCS | C1 ◁ C22 ◁ #120 | |
9088 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
210 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#120×AGL(1,𝔽7), D3×D7×B(4,𝔽2), D7×C3⋊D3×#120, … |
| maximal normal subgroup of | D3×#120×AGL(1,𝔽7), D3×D7×B(4,𝔽2) |
| maximal quotient of | D3×D7×B(4,𝔽2), D3×D7×#453, D7×C3⋊D3×#120, … |
Past the SmallGroups library coverage — no SmallGroups id.