Finite Group DatabasebetaFinite Group Databasebeta| order | 7914 |
| automorphism | Aut(G) order 10430652 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3957 |
| unambiguous semidirect product | C3⋊D1319 |
| unambiguous semidirect product | C1319⋊D3 |
| Fitting, socle, derived, Hall | C3×C1319 ⋊ C2 |
| Sylow | C1319 ⋊ D3 |
| Sylow | C3 ⋊ D1319 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C1319 | C2 |
| LCS | G ▷ C3×C1319 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,1319|b^a=b^2,c^a=c^13181980 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D1319, C2×D3957, D11871, … |
| maximal normal subgroup of | D3×D1319, C2×D3957, C3×D3957 |
| maximal quotient of | Dic3957, C2×D3957, D11871, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7914, 3);