Finite Group DatabasebetaFinite Group Databasebeta| order | 31084 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C19⋊#13109888 |
| Fitting, socle, derived, Hall | C19×C409 ⋊ C4 |
| Sylow | C409 ⋊ Dic19 |
| Sylow | C19 ⋊ #13109888 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C19×C409 | C4 |
| prime radical, cosocle | C19×D409 | C2 |
| LCS | G ▷ C19×C409 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7771 |
Polycyclic presentation:
2^2,19,409|a^2=b,c^a=c^18,d^a=d^266,d^b=d^4081960 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31084, 7);