Finite Group DatabasebetaFinite Group Databasebeta| order | 5594 |
| automorphism | Aut(G) order 7820412 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2797 |
| unambiguous semidirect product | C2797⋊C2 |
| Fitting, socle, derived, Sylow | C2797 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C2797 | C2 |
| LCS | G ▷ C2797 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,2797|b^a=b^27961400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #26014123, C2×D2797, D2797⋊C3, … |
| maximal normal subgroup of | #26014123, C2×D2797, D2797⋊C3, … |
| maximal quotient of | Dic2797, C2×D2797, C3×D2797, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5594, 1);