Finite Group DatabasebetaFinite Group Databasebeta| order | 5618 |
| automorphism | Aut(G) order 7741604 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2809 |
| unambiguous semidirect product | C2809⋊C2 |
| Fitting, derived, Sylow | C2809 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C2809 | C2 |
| Frattini, socle | C53 | D53 |
| LCS | G ▷ C2809 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
Polycyclic presentation:
2,53^2|b^53=c,b^a=b^52c^52,c^a=c^521406 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #26014492, C2×D2809, C3×D2809, … |
| maximal normal subgroup of | #26014492, C2×D2809, C3×D2809, … |
| maximal quotient of | Dic2809, C2×D2809, C3×D2809, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5618, 1);