Finite Group DatabasebetaFinite Group Databasebeta| order | 8274 |
| automorphism | Aut(G) order 9730224 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4137 |
| unambiguous semidirect product | C3⋊D1379 |
| unambiguous semidirect product | C7⋊D591 |
| unambiguous semidirect product | C197⋊D21 |
| Fitting, socle, derived, Hall | C3×C7×C197 ⋊ C2 |
| Hall | C7×C197 ⋊ D3 |
| Hall | C3×C197 ⋊ D7 |
| Sylow | C197 ⋊ D21 |
| Hall | C3×C7 ⋊ D197 |
| Sylow | C7 ⋊ D591 |
| Sylow | C3 ⋊ D1379 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C7×C197 | C2 |
| LCS | G ▷ C3×C7×C197 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,197|b^a=b^2,c^a=c^6,d^a=d^1962070 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D21×D197, D7×D591, D3×D1379, … |
| maximal normal subgroup of | D21×D197, D7×D591, D3×D1379, … |
| maximal quotient of | Dic4137, C2×D4137, D12411, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8274, 10);