Finite Group DatabasebetaFinite Group Databasebeta| order | 8412 |
| automorphism | Aut(G) order 5888400 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D4206 |
| direct product | C2×D2103 |
| unambiguous semidirect product | (C2×C3)⋊D701 |
| unambiguous semidirect product | (C2×C701)⋊D3 |
| Fitting, socle | C2×C3×C701 ⋊ C2 |
| derived, Hall | C3×C701 ⋊ C22 |
| Sylow | C701 ⋊ C2×D3 |
| Sylow | C3 ⋊ C2×D701 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2103 |
| commutator, hypocenter | C3×C701 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C701 | C2 |
| LCS | G ▷ C3×C701 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
2106 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D6309, D3×D2103, C2×C3×D2103, … |
| maximal normal subgroup of | C2×C3×D2103, D8412 |
| maximal quotient of | C2×D6309, D3×D2103, C2×C3×D2103, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8412, 10);