Finite Group DatabasebetaFinite Group Databasebeta| order | 34146 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C2×C3×#19151018 |
| Fitting, socle | C2×C3×C7×C271 ⋊ C3 |
| derived, Hall | C7×C271 ⋊ C2×C32 |
| Hall | C2×C7×C271 ⋊ C32 |
| Hall | C2×C271 ⋊ C3×ΓL(1,𝔽8) |
| Sylow | C271 ⋊ C2×C3×ΓL(1,𝔽8) |
| Hall | C2×C7 ⋊ C3×C271⋊C3 |
| Sylow | C7 ⋊ C2×C3×C271⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #19151018 |
| commutator, cosocle, hypocenter | C7×C271 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C7×C271 | C3 |
| LCS | G ▷ C7×C271 | |
| UCS | C1 ◁ C2×C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11382 |
3810 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34146, 73);