Finite Group DatabasebetaFinite Group Databasebeta| order | 5458 |
| automorphism | Aut(G) order 7444712 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2729 |
| unambiguous semidirect product | C2729⋊C2 |
| Fitting, socle, derived, Sylow | C2729 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C2729 | C2 |
| LCS | G ▷ C2729 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,2729|b^a=b^27281366 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #24926337, C2×D2729, C3×D2729, … |
| maximal normal subgroup of | #24926337, C2×D2729, C3×D2729, … |
| maximal quotient of | Dic2729, C2×D2729, C3×D2729, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5458, 1);