Finite Group DatabasebetaFinite Group Databasebeta| order | 10534 |
| automorphism | Aut(G) order 26419272 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5267 |
| unambiguous semidirect product | C23⋊D229 |
| unambiguous semidirect product | C229⋊D23 |
| Fitting, socle, derived, Hall | C23×C229 ⋊ C2 |
| Sylow | C229 ⋊ D23 |
| Sylow | C23 ⋊ D229 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C23×C229 | C2 |
| LCS | G ▷ C23×C229 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,23,229|b^a=b^22,c^a=c^2282635 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D23×D229, C2×D5267, C3×D5267, … |
| maximal normal subgroup of | D23×D229, C2×D5267, C3×D5267, … |
| maximal quotient of | Dic5267, C2×D5267, C3×D5267, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10534, 3);