Finite Group DatabasebetaFinite Group Databasebeta| order | 31692 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #30629294⋊C2 |
| unambiguous semidirect product | #30629298⋊C2 |
| unambiguous semidirect product | #30629302⋊C2 |
| Fitting, socle, derived, Hall | C19×C139 ⋊ C22×C3 |
| Hall | D19×D139 ⋊ C3 |
| Hall | #21463700 ⋊ C22 |
| Sylow | C139 ⋊ C2×D19⋊C3 |
| Sylow | C19 ⋊ C2×D139⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C19×C139 | C22×C3 |
| LCS | G ▷ C19×C139 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2641 |
Polycyclic presentation:
2^2,3,19,139|e^a=e^138,d^b=d^18,d^c=d^7,e^c=e^42271 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31692, 26);