Finite Group DatabasebetaFinite Group Databasebeta| order | 10082 |
| automorphism | Aut(G) order 25053770 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5041 |
| unambiguous semidirect product | C5041⋊C2 |
| Fitting, derived, Sylow | C5041 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5041 | C2 |
| Frattini, socle | C71 | D71 |
| LCS | G ▷ C5041 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
Polycyclic presentation:
2,71^2|b^71=c,b^a=b^70c^70,c^a=c^702522 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D5041, C3×D5041, D15123, … |
| maximal normal subgroup of | C2×D5041, C3×D5041 |
| maximal quotient of | Dic5041, C2×D5041, C3×D5041, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10082, 1);