Finite Group DatabasebetaFinite Group Databasebeta| order | 19995 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #16860688⋊C5 |
| Fitting, socle, derived, Hall | C31×C43 ⋊ C3×C5 |
| Hall | C43×ΓL(1,𝔽32) ⋊ C3 |
| Hall | #16860688 ⋊ C5 |
| Hall | ΓL(1,𝔽32) ⋊ C43⋊C3 |
| Sylow | C43 ⋊ (C31⋊C3)⋊C5 |
| Sylow | C31 ⋊ C5×C43⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C31×C43 | C3×C5 |
| LCS | G ▷ C31×C43 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1333 |
Polycyclic presentation:
3,5,31,43|c^a=c^25,d^a=d^6,c^b=c^16171 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19995, 10);