Finite Group DatabasebetaFinite Group Databasebeta| order | 16430 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C53⋊(D31⋊C5) |
| unambiguous semidirect product | ΓL(1,𝔽32)⋊D53 |
| unambiguous semidirect product | D1643⋊C5 |
| Fitting, socle, derived, Hall | C31×C53 ⋊ C2×C5 |
| Hall | C53×ΓL(1,𝔽32) ⋊ C2 |
| Hall | D1643 ⋊ C5 |
| Hall | ΓL(1,𝔽32) ⋊ D53 |
| Sylow | C53 ⋊ D31⋊C5 |
| Sylow | C31 ⋊ C5×D53 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C31×C53 | C2×C5 |
| LCS | G ▷ C31×C53 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1643 |
Polycyclic presentation:
2,5,31,53|c^a=c^30,d^a=d^52,c^b=c^16299 conjugacy classes — view the full character table.
| maximal subgroup of | D53×D31⋊C5, C2×C53⋊(D31⋊C5) |
| maximal normal subgroup of | D53×D31⋊C5, C2×C53⋊(D31⋊C5) |
| maximal quotient of | ΓL(1,𝔽32)⋊Dic53, C2×C53⋊(D31⋊C5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16430, 12);