Finite Group DatabasebetaFinite Group Databasebeta| order | 5402 |
| isoclinism | isoclinic class of D37 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C73 · Schur multiplier (H2) = C1 |
| direct product | C73×D37 |
| unambiguous semidirect product | C37⋊(C2×C73) |
| Fitting, socle, Hall | C37×C73 ⋊ C2 |
| derived, Sylow | C37 ⋊ C2×C73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C73 | D37 |
| commutator, hypocenter | C37 | C2×C73 |
| Frattini | C1 | G |
| Fitting, socle | C37×C73 | C2 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C73 | |
8 conjugacy classes of subgroups.
1460 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C73×D37, C73×D111, D37×C73⋊C3, … |
| maximal normal subgroup of | C3×C73×D37, D37×C73⋊C3, C73×D37⋊C3, … |
| maximal quotient of | C3×C73×D37, C73×D111, C5×C73×D37, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5402, 1);