Finite Group DatabasebetaFinite Group Databasebeta| order | 10412 |
| automorphism | Aut(G) order 12744288 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D5206 |
| direct product | C2×D2603 |
| unambiguous semidirect product | (C2×C19)⋊D137 |
| unambiguous semidirect product | (C2×C137)⋊D19 |
| Fitting, socle | C2×C19×C137 ⋊ C2 |
| derived, Hall | C19×C137 ⋊ C22 |
| Sylow | C137 ⋊ C2×D19 |
| Sylow | C19 ⋊ C2×D137 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2603 |
| commutator, cosocle, hypocenter | C19×C137 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C19×C137 | C2 |
| LCS | G ▷ C19×C137 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
2606 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×(C19⋊C3)⋊D137, D3×D2603, C2×C3×D2603, … |
| maximal normal subgroup of | C2×(C19⋊C3)⋊D137, C2×C3×D2603, D10412 |
| maximal quotient of | D3×D2603, C2×C3×D2603, C2×D7809, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10412, 9);