Finite Group DatabasebetaFinite Group Databasebeta| order | 10412 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C19⋊#10587739 |
| Fitting, socle, derived, Hall | C19×C137 ⋊ C4 |
| Sylow | C137 ⋊ Dic19 |
| Sylow | C19 ⋊ #10587739 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C19×C137 | C4 |
| prime radical, cosocle | C19×D137 | C2 |
| LCS | G ▷ C19×C137 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,19,137|a^2=b,c^a=c^18,d^a=d^100,d^b=d^136668 conjugacy classes — view the full character table.
| maximal subgroup of | (C19⋊C3)⋊#10587739, C3×C19⋊#10587739, C3⋊(C19⋊#10587739) |
| maximal normal subgroup of | (C19⋊C3)⋊#10587739, C3×C19⋊#10587739 |
| maximal quotient of | C3×C19⋊#10587739, C3⋊(C19⋊#10587739) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10412, 7);