Finite Group DatabasebetaFinite Group Databasebeta| order | 11626 |
| automorphism | Aut(G) order 33785156 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5813 |
| unambiguous semidirect product | C5813⋊C2 |
| Fitting, socle, derived, Sylow | C5813 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5813 | C2 |
| LCS | G ▷ C5813 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,5813|b^a=b^58122908 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37551362, C2×D5813, C3×D5813, … |
| maximal normal subgroup of | #37551362, C2×D5813, C3×D5813 |
| maximal quotient of | Dic5813, C2×D5813, C3×D5813, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11626, 1);