Finite Group DatabasebetaFinite Group Databasebeta| order | 2646 |
| isoclinism | isoclinic class of 3−1+2⋊D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×3−1+2⋊D7 |
| Fitting, Hall | C72×3−1+2 ⋊ C2 |
| derived | C7×C9 ⋊ C2×C3×C7 |
| Sylow | C72 ⋊ AGL(1,ℤ/9) |
| Sylow | 3−1+2 ⋊ C7×D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | 3−1+2⋊D7 |
| commutator, cosocle, hypocenter | C7×C9 | C2×C3×C7 |
| Frattini | C3 | C3×C7×D21 |
| Fitting | C72×3−1+2 | C2 |
| socle | C3×C72 | C3×D3 |
| LCS | G ▷ C7×C9 | |
| UCS | C1 ◁ C7 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 126 |
301 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72229923, C7×D7×AGL(1,ℤ/9), D7×3−1+2⋊D7, … |
| maximal normal subgroup of | #72229923, C7×D7×AGL(1,ℤ/9), D7×3−1+2⋊D7, … |
Past the SmallGroups library coverage — no SmallGroups id.