Finite Group DatabasebetaFinite Group Databasebeta| order | 5740 |
| isoclinism | isoclinic class of D35 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C41 · Schur multiplier (H2) = C1 |
| direct product | C41×Dic35 |
| unambiguous semidirect product | C7⋊(Dic5×C41) |
| derived, Hall | C5×C7 ⋊ C4×C41 |
| Hall | C5×C7×C41 ⋊ C4 |
| Hall | C7×C41 ⋊ Dic5 |
| Hall | C5×C41 ⋊ Dic7 |
| Sylow | C7 ⋊ Dic5×C41 |
| Sylow | C5 ⋊ Dic7×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C41 | D35 |
| commutator, hypocenter | C5×C7 | C4×C41 |
| Frattini | C2 | C41×D35 |
| Fitting, socle | C2×C5×C7×C41 | C2 |
| LCS | G ▷ C5×C7 | |
| UCS | C1 ◁ C2×C41 | |
24 conjugacy classes of subgroups.
1558 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C41×Dic35, C41×Dic105, C41×ΓL(1,𝔽8)⋊Dic5, … |
| maximal normal subgroup of | C3×C41×Dic35, C41×ΓL(1,𝔽8)⋊Dic5, Dic35×C41⋊C5, … |
| maximal quotient of | C3×C41×Dic35, C41×Dic105, C41×Dic175, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5740, 8);