Finite Group DatabasebetaFinite Group Databasebeta| order | 735 |
| isoclinism | isoclinic class of #3862 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C7 |
| direct product | C5×#3862 |
| Fitting, socle, Hall | C5×C72 ⋊ C3 |
| derived, Sylow | C72 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #3862 |
| commutator, cosocle, hypocenter | C72 | C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72 | C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C5 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 105 |
95 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(735, 5);