Finite Group DatabasebetaFinite Group Databasebeta| order | 3402 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C33 |
| direct product | D7×#6891 |
| Fitting, Hall | C7×#6891 ⋊ C2 |
| Sylow | C7 ⋊ C2×#6891 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C33×D7 |
| commutator, socle, cosocle | C32×C7 | C2×C33 |
| Fitting | C7×#6891 | C2 |
| prime radical | C34×D7 | C3 |
| hypercenter | #6891 | D7 |
| hypocenter | C7 | C2×#6891 |
| LCS | G ▷ C32×C7 ▷ C7 | |
| UCS | C1 ◁ C32 ◁ #6891 | |
504 conjugacy classes of subgroups.
| transitive degree | μt(G) = 189 |
255 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#10624749, AGL(1,𝔽7)×#6891, #72249153, … |
| maximal normal subgroup of | D7×#10624749, AGL(1,𝔽7)×#6891, #72249153, … |
Past the SmallGroups library coverage — no SmallGroups id.