Finite Group DatabasebetaFinite Group Databasebeta| order | 7394 |
| automorphism | Aut(G) order 13664112 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3697 |
| unambiguous semidirect product | C3697⋊C2 |
| Fitting, socle, derived, Sylow | C3697 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3697 | C2 |
| LCS | G ▷ C3697 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,3697|b^a=b^36961850 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28414395, C2×D3697, D3697⋊C3, … |
| maximal normal subgroup of | #28414395, C2×D3697, D3697⋊C3, … |
| maximal quotient of | Dic3697, C2×D3697, C3×D3697, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7394, 1);