Finite Group DatabasebetaFinite Group Databasebeta| order | 31692 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C139⋊C3)⋊Dic19 |
| derived, Hall | C19×C139 ⋊ C3×C4 |
| Hall | Dic2641 ⋊ C3 |
| Hall | C19×C139⋊C3 ⋊ C4 |
| Hall | C139⋊C3 ⋊ Dic19 |
| Sylow | C139 ⋊ C3×Dic19 |
| Sylow | C19 ⋊ (C139⋊C3)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | (C139⋊C3)⋊D19 |
| commutator, hypocenter | C19×C139 | C3×C4 |
| Fitting, socle, cosocle | C2×C19×C139 | C2×C3 |
| prime radical | C2×C19×C139⋊C3 | C2 |
| LCS | G ▷ C19×C139 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10564 |
Polycyclic presentation:
2,3,19,139,2|a^2=e,c^a=c^18,d^a=d^138,d^b=d^96940 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31692, 21);