Finite Group DatabasebetaFinite Group Databasebeta| order | 10222 |
| automorphism | Aut(G) order 24655464 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5111 |
| unambiguous semidirect product | C19⋊D269 |
| unambiguous semidirect product | C269⋊D19 |
| Fitting, socle, derived, Hall | C19×C269 ⋊ C2 |
| Sylow | C269 ⋊ D19 |
| Sylow | C19 ⋊ D269 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C19×C269 | C2 |
| LCS | G ▷ C19×C269 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,19,269|b^a=b^18,c^a=c^2682557 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D19×D269, C2×D5111, C3×D5111, … |
| maximal normal subgroup of | D19×D269, C2×D5111, C3×D5111, … |
| maximal quotient of | Dic5111, C2×D5111, C3×D5111, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10222, 3);