Finite Group DatabasebetaFinite Group Databasebeta| order | 31692 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D57⋊D139 |
| unambiguous semidirect product | D417⋊D19 |
| unambiguous semidirect product | D2641⋊D3 |
| Fitting, socle, derived, Hall | C3×C19×C139 ⋊ C22 |
| Hall | C19×C139 ⋊ C2×D3 |
| Hall | C3×C139 ⋊ C2×D19 |
| Sylow | C139 ⋊ D3×D19 |
| Hall | C3×C19 ⋊ C2×D139 |
| Sylow | C19 ⋊ D3×D139 |
| Sylow | C3 ⋊ D19×D139 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C19×C139 | C22 |
| LCS | G ▷ C3×C19×C139 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7923 |
Polycyclic presentation:
2^2,3,19,139|d^a=d^18,e^a=e^138,c^b=c^2,d^b=d^182103 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31692, 48);