Finite Group DatabasebetaFinite Group Databasebeta| order | 11182 |
| automorphism | Aut(G) order 31253690 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5591 |
| unambiguous semidirect product | C5591⋊C2 |
| Fitting, socle, derived, Sylow | C5591 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5591 | C2 |
| LCS | G ▷ C5591 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,5591|b^a=b^55902797 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D5591, C3×D5591, D16773 |
| maximal normal subgroup of | C2×D5591, C3×D5591 |
| maximal quotient of | Dic5591, C2×D5591, C3×D5591, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11182, 1);