Finite Group DatabasebetaFinite Group Databasebeta| order | 34524 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽8)×C3⋊#10587739 |
| unambiguous semidirect product | C3⋊(ΓL(1,𝔽8)×#10587739) |
| unambiguous semidirect product | (C7×C3⋊#10587739)⋊C3 |
| Fitting, socle, derived | C3×C7×C137 ⋊ C3×C4 |
| Hall | C3×ΓL(1,𝔽8)×C137 ⋊ C4 |
| Hall | C7×C137 ⋊ C3×Dic3 |
| Sylow | C137 ⋊ Dic3×ΓL(1,𝔽8) |
| Hall | C3×ΓL(1,𝔽8) ⋊ #10587739 |
| Sylow | C7 ⋊ C3×C3⋊#10587739 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C7×C137 | C3×C4 |
| prime radical | C3×ΓL(1,𝔽8)×D137 | C2 |
| cosocle | C3×C7×D137 | C2×C3 |
| LCS | G ▷ C3×C7×C137 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2877 |
540 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34524, 71);