Finite Group DatabasebetaFinite Group Databasebeta| order | 10774 |
| automorphism | Aut(G) order 29014382 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5387 |
| unambiguous semidirect product | C5387⋊C2 |
| Fitting, socle, derived, Sylow | C5387 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5387 | C2 |
| LCS | G ▷ C5387 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,5387|b^a=b^53862695 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D5387, C3×D5387, D16161 |
| maximal normal subgroup of | C2×D5387, C3×D5387 |
| maximal quotient of | Dic5387, C2×D5387, C3×D5387, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10774, 1);