Finite Group DatabasebetaFinite Group Databasebeta| order | 740 |
| isoclinism | isoclinic class of #3866 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#3866 |
| Fitting, socle, Hall | C5×C37 ⋊ C4 |
| derived, Sylow | C37 ⋊ C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #3866 |
| commutator, hypocenter | C37 | C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C37 | C4 |
| prime radical | C5×D37 | C2 |
| cosocle | D37 | C2×C5 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C5 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 185 |
65 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#3866, C2×C5×#3866, C5×#3866⋊C3, … |
| maximal normal subgroup of | D5×#3866, C2×C5×#3866, C5×#3866⋊C3, … |
| maximal quotient of | C5×#64438, C2×C5×#3866, C3×C5×#3866, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(740, 5);