Finite Group DatabasebetaFinite Group Databasebeta| order | 35175 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C52⋊#13064105 |
| Fitting, socle, derived, Hall | C52×C7×C67 ⋊ C3 |
| Hall | C52×C67 ⋊ ΓL(1,𝔽8) |
| Hall | C7×C67 ⋊ C52⋊C3 |
| Hall | C52×C7 ⋊ C67⋊C3 |
| Sylow | C67 ⋊ C7⋊(C52⋊C3) |
| Sylow | C52 ⋊ #13064105 |
| Sylow | C7 ⋊ C52⋊(C67⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C7×C67 | C3 |
| LCS | G ▷ C52×C7×C67 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7035 |
Polycyclic presentation:
3,5^2,7,67|b^a=b^3c^2,c^a=bc,d^a=d^2,e^a=e^373911 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35175, 11);