Finite Group DatabasebetaFinite Group Databasebeta| order | 5402 |
| automorphism | Aut(G) order 7000992 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2701 |
| unambiguous semidirect product | C37⋊D73 |
| unambiguous semidirect product | C73⋊D37 |
| Fitting, socle, derived, Hall | C37×C73 ⋊ C2 |
| Sylow | C73 ⋊ D37 |
| Sylow | C37 ⋊ D73 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C37×C73 | C2 |
| LCS | G ▷ C37×C73 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,37,73|b^a=b^36,c^a=c^721352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D2701, D8103, (C73⋊C3)⋊D37, … |
| maximal normal subgroup of | C3×D2701, (C73⋊C3)⋊D37, (C37⋊C3)⋊D73, … |
| maximal quotient of | C3×D2701, D8103, C5×D2701, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5402, 3);