Finite Group DatabasebetaFinite Group Databasebeta| order | 10762 |
| automorphism | Aut(G) order 28949780 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5381 |
| unambiguous semidirect product | C5381⋊C2 |
| Fitting, socle, derived, Sylow | C5381 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5381 | C2 |
| LCS | G ▷ C5381 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,5381|b^a=b^53802692 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36340270, C2×D5381, C3×D5381, … |
| maximal normal subgroup of | #36340270, C2×D5381, C3×D5381 |
| maximal quotient of | Dic5381, C2×D5381, C3×D5381, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10762, 1);