Finite Group DatabasebetaFinite Group Databasebeta| order | 8427 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C53 |
| unambiguous semidirect product | C532⋊C3 |
| Fitting, socle, derived, Sylow | C532 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C532 | C3 |
| LCS | G ▷ C532 | |
| UCS | C1 | |
22 conjugacy classes of subgroups.
Polycyclic presentation:
3,53^2|b^a=b^31c^24,c^a=b^5c^21939 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8427, 2);