Finite Group DatabasebetaFinite Group Databasebeta| order | 7354 |
| automorphism | Aut(G) order 13516652 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3677 |
| unambiguous semidirect product | C3677⋊C2 |
| Fitting, socle, derived, Sylow | C3677 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3677 | C2 |
| LCS | G ▷ C3677 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,3677|b^a=b^36761840 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28413732, C2×D3677, C3×D3677, … |
| maximal normal subgroup of | #28413732, C2×D3677, C3×D3677, … |
| maximal quotient of | Dic3677, C2×D3677, C3×D3677, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7354, 1);