Finite Group DatabasebetaFinite Group Databasebeta| order | 35175 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C67 · Schur multiplier (H2) = C5 |
| direct product | C67×C7⋊(C52⋊C3) |
| unambiguous semidirect product | C7⋊(C67×C52⋊C3) |
| unambiguous semidirect product | C52⋊(ΓL(1,𝔽8)×C67) |
| Fitting, socle, Hall | C52×C7×C67 ⋊ C3 |
| derived, Hall | C52×C7 ⋊ C3×C67 |
| Hall | C52×C67 ⋊ ΓL(1,𝔽8) |
| Hall | C7×C67 ⋊ C52⋊C3 |
| Sylow | C52 ⋊ ΓL(1,𝔽8)×C67 |
| Sylow | C7 ⋊ C67×C52⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C67 | C7⋊(C52⋊C3) |
| commutator, cosocle, hypocenter | C52×C7 | C3×C67 |
| Frattini | C1 | G |
| Fitting, socle | C52×C7×C67 | C3 |
| LCS | G ▷ C52×C7 | |
| UCS | C1 ◁ C67 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7035 |
4087 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35175, 9);