Finite Group DatabasebetaFinite Group Databasebeta| order | 5638 |
| automorphism | Aut(G) order 7943942 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2819 |
| unambiguous semidirect product | C2819⋊C2 |
| Fitting, socle, derived, Sylow | C2819 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C2819 | C2 |
| LCS | G ▷ C2819 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,2819|b^a=b^28181411 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D2819, C3×D2819, D8457, … |
| maximal normal subgroup of | C2×D2819, C3×D2819, C5×D2819 |
| maximal quotient of | Dic2819, C2×D2819, C3×D2819, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5638, 1);