Finite Group DatabasebetaFinite Group Databasebeta| order | 34524 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3⋊AGL(1,𝔽7)×D137 |
| unambiguous semidirect product | (C3×D137)⋊AGL(1,𝔽7) |
| unambiguous semidirect product | (ΓL(1,𝔽8)×D137)⋊D3 |
| unambiguous semidirect product | (D21×D137)⋊C3 |
| Fitting, socle, derived | C3×C7×C137 ⋊ C22×C3 |
| Hall | C3×ΓL(1,𝔽8)×C137 ⋊ C22 |
| Hall | C7×C137 ⋊ C2×C3×D3 |
| Sylow | C137 ⋊ C2×C3⋊AGL(1,𝔽7) |
| Hall | C3×ΓL(1,𝔽8) ⋊ C2×D137 |
| Sylow | C7 ⋊ C3×D3×D137 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C7×C137 | C22×C3 |
| LCS | G ▷ C3×C7×C137 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2877 |
840 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34524, 66);