Finite Group DatabasebetaFinite Group Databasebeta| order | 10010 |
| automorphism | Aut(G) order 14414400 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5005 |
| unambiguous semidirect product | C5⋊D1001 |
| unambiguous semidirect product | C7⋊D715 |
| unambiguous semidirect product | C11⋊D455 |
| unambiguous semidirect product | C13⋊D385 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C7×C11×C13 | C2 |
| LCS | G ▷ C5×C7×C11×C13 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,7,11,13|b^a=b^4,c^a=c^6,d^a=d^10,e^a=e^122504 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D13×D385, D11×D455, D35×D143, … |
| maximal normal subgroup of | D13×D385, D11×D455, D35×D143, … |
| maximal quotient of | Dic5005, C2×D5005, C3×D5005, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10010, 17);