Finite Group DatabasebetaFinite Group Databasebeta| order | 10834 |
| automorphism | Aut(G) order 29338472 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5417 |
| unambiguous semidirect product | C5417⋊C2 |
| Fitting, socle, derived, Sylow | C5417 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5417 | C2 |
| LCS | G ▷ C5417 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,5417|b^a=b^54162710 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36343552, C2×D5417, C3×D5417, … |
| maximal normal subgroup of | #36343552, C2×D5417, C3×D5417 |
| maximal quotient of | Dic5417, C2×D5417, C3×D5417, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10834, 1);