Finite Group DatabasebetaFinite Group Databasebeta| order | 11294 |
| automorphism | Aut(G) order 31882962 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5647 |
| unambiguous semidirect product | C5647⋊C2 |
| Fitting, socle, derived, Sylow | C5647 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5647 | C2 |
| LCS | G ▷ C5647 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,5647|b^a=b^56462825 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D5647, D5647⋊C3, C3×D5647, … |
| maximal normal subgroup of | C2×D5647, D5647⋊C3, C3×D5647 |
| maximal quotient of | Dic5647, C2×D5647, C3×D5647, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11294, 1);