Finite Group DatabasebetaFinite Group Databasebeta| order | 10754 |
| automorphism | Aut(G) order 27293652 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5377 |
| unambiguous semidirect product | C19⋊D283 |
| unambiguous semidirect product | C283⋊D19 |
| Fitting, socle, derived, Hall | C19×C283 ⋊ C2 |
| Sylow | C283 ⋊ D19 |
| Sylow | C19 ⋊ D283 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C19×C283 | C2 |
| LCS | G ▷ C19×C283 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,19,283|b^a=b^18,c^a=c^2822690 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D19×D283, C2×D5377, C3×D5377, … |
| maximal normal subgroup of | D19×D283, C2×D5377, C3×D5377, … |
| maximal quotient of | Dic5377, C2×D5377, C3×D5377, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10754, 3);