Finite Group DatabasebetaFinite Group Databasebeta| order | 7470 |
| isoclinism | isoclinic class of D83 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3 |
| direct product | C32×C5×D83 |
| unambiguous semidirect product | C83⋊(C2×C32×C5) |
| Fitting, socle, Hall | C32×C5×C83 ⋊ C2 |
| derived, Sylow | C83 ⋊ C2×C32×C5 |
| Hall | C32×C83 ⋊ C2×C5 |
| Hall | C5×C83 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C5 | D83 |
| commutator, hypocenter | C83 | C2×C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C83 | C2 |
| LCS | G ▷ C83 | |
| UCS | C1 ◁ C32×C5 | |
48 conjugacy classes of subgroups.
1935 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×D5×D83, C3×C5×D3×D83, C3×D15×D83, … |
| maximal normal subgroup of | C32×D5×D83, C3×C5×D3×D83, C3×D15×D83, … |
| maximal quotient of | C32×C5×Dic83, C2×C32×C5×D83, C32×C25×D83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7470, 10);