Finite Group DatabasebetaFinite Group Databasebeta| order | 7622 |
| automorphism | Aut(G) order 13993992 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3811 |
| unambiguous semidirect product | C37⋊D103 |
| unambiguous semidirect product | C103⋊D37 |
| Fitting, socle, derived, Hall | C37×C103 ⋊ C2 |
| Sylow | C103 ⋊ D37 |
| Sylow | C37 ⋊ D103 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C37×C103 | C2 |
| LCS | G ▷ C37×C103 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,37,103|b^a=b^36,c^a=c^1021907 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D37×D103, C2×D3811, C3×D3811, … |
| maximal normal subgroup of | D37×D103, C2×D3811, C3×D3811, … |
| maximal quotient of | Dic3811, C2×D3811, C3×D3811, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7622, 3);