Finite Group DatabasebetaFinite Group Databasebeta| order | 31236 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D57⋊D137 |
| unambiguous semidirect product | D411⋊D19 |
| unambiguous semidirect product | D2603⋊D3 |
| Fitting, socle, derived, Hall | C3×C19×C137 ⋊ C22 |
| Hall | C19×C137 ⋊ C2×D3 |
| Hall | C3×C137 ⋊ C2×D19 |
| Sylow | C137 ⋊ D3×D19 |
| Hall | C3×C19 ⋊ C2×D137 |
| Sylow | C19 ⋊ D3×D137 |
| Sylow | C3 ⋊ D19×D137 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C19×C137 | C22 |
| LCS | G ▷ C3×C19×C137 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7809 |
Polycyclic presentation:
2^2,3,19,137|d^a=d^18,e^a=e^136,c^b=c^2,d^b=d^182073 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31236, 30);