Finite Group DatabasebetaFinite Group Databasebeta| order | 10078 |
| automorphism | Aut(G) order 25386482 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5039 |
| unambiguous semidirect product | C5039⋊C2 |
| Fitting, socle, derived, Sylow | C5039 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5039 | C2 |
| LCS | G ▷ C5039 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,5039|b^a=b^50382521 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D5039, C3×D5039, D15117 |
| maximal normal subgroup of | C2×D5039, C3×D5039 |
| maximal quotient of | Dic5039, C2×D5039, C3×D5039, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10078, 1);