Finite Group DatabasebetaFinite Group Databasebeta| order | 3402 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C36 |
| direct product | D7×C32⋊H(3,𝔽3) |
| Fitting, Hall | C7×C32⋊H(3,𝔽3) ⋊ C2 |
| Sylow | C7 ⋊ C2×C32⋊H(3,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C33×D7 |
| commutator, socle, cosocle | C32×C7 | C2×C33 |
| Fitting | C7×C32⋊H(3,𝔽3) | C2 |
| hypercenter | C32⋊H(3,𝔽3) | D7 |
| hypocenter | C7 | C2×C32⋊H(3,𝔽3) |
| LCS | G ▷ C32×C7 ▷ C7 | |
| UCS | C1 ◁ C32 ◁ C32⋊H(3,𝔽3) | |
756 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)×C32⋊H(3,𝔽3), #72249151, … |
| maximal normal subgroup of | D7×#10624749, AGL(1,𝔽7)×C32⋊H(3,𝔽3), #72249151, … |
| maximal quotient of | D7×#10624749 |
Past the SmallGroups library coverage — no SmallGroups id.