Finite Group DatabasebetaFinite Group Databasebeta| order | 10246 |
| automorphism | Aut(G) order 25451064 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5123 |
| unambiguous semidirect product | C47⋊D109 |
| unambiguous semidirect product | C109⋊D47 |
| Fitting, socle, derived, Hall | C47×C109 ⋊ C2 |
| Sylow | C109 ⋊ D47 |
| Sylow | C47 ⋊ D109 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C47×C109 | C2 |
| LCS | G ▷ C47×C109 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,47,109|b^a=b^46,c^a=c^1082563 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D47×D109, C2×D5123, C3×D5123, … |
| maximal normal subgroup of | D47×D109, C2×D5123, C3×D5123, … |
| maximal quotient of | Dic5123, C2×D5123, C3×D5123, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10246, 3);