Finite Group DatabasebetaFinite Group Databasebeta| order | 7402 |
| automorphism | Aut(G) order 13693700 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3701 |
| unambiguous semidirect product | C3701⋊C2 |
| Fitting, socle, derived, Sylow | C3701 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3701 | C2 |
| LCS | G ▷ C3701 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,3701|b^a=b^37001852 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28414447, C2×D3701, C3×D3701, … |
| maximal normal subgroup of | #28414447, C2×D3701, C3×D3701, … |
| maximal quotient of | Dic3701, C2×D3701, C3×D3701, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7402, 1);