Finite Group DatabasebetaFinite Group Databasebeta| order | 7918 |
| automorphism | Aut(G) order 15107544 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3959 |
| unambiguous semidirect product | C37⋊D107 |
| unambiguous semidirect product | C107⋊D37 |
| Fitting, socle, derived, Hall | C37×C107 ⋊ C2 |
| Sylow | C107 ⋊ D37 |
| Sylow | C37 ⋊ D107 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C37×C107 | C2 |
| LCS | G ▷ C37×C107 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,37,107|b^a=b^36,c^a=c^1061981 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D37×D107, C2×D3959, C3×D3959, … |
| maximal normal subgroup of | D37×D107, C2×D3959, C3×D3959, … |
| maximal quotient of | Dic3959, C2×D3959, C3×D3959, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7918, 3);