Finite Group DatabasebetaFinite Group Databasebeta| order | 3402 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C3 |
| direct product | C7×#92338 |
| Fitting, Hall | C7×C32⋊H(3,𝔽3) ⋊ C2 |
| derived, Sylow | C32⋊H(3,𝔽3) ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C32×C7 | C3⋊(C3⋊D3) |
| commutator, cosocle, hypocenter | C32⋊H(3,𝔽3) | C2×C7 |
| Frattini | C32 | C7×C3⋊(C3⋊D3) |
| Fitting | C7×C32⋊H(3,𝔽3) | C2 |
| LCS | G ▷ C32⋊H(3,𝔽3) | |
| UCS | C1 ◁ C32×C7 | |
534 conjugacy classes of subgroups.
| transitive degree | μt(G) = 189 |
273 conjugacy classes. The character table is too large to display.
| maximal subgroup of | ΓL(1,𝔽8)×#92338, D7×#92338 |
| maximal normal subgroup of | ΓL(1,𝔽8)×#92338, D7×#92338 |
| maximal quotient of | C7×#13091120 |
Past the SmallGroups library coverage — no SmallGroups id.