Finite Group DatabasebetaFinite Group Databasebeta| order | 31772 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C13 |
| unambiguous semidirect product | C47⋊#10621729 |
| Fitting, socle, derived, Hall | C132×C47 ⋊ C4 |
| Sylow | C132 ⋊ Dic47 |
| Sylow | C47 ⋊ #10621729 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C132×C47 | C4 |
| prime radical, cosocle | C47×C13⋊D13 | C2 |
| LCS | G ▷ C132×C47 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1222 |
Polycyclic presentation:
2^2,13^2,47|a^2=b,c^a=c^5,d^a=d^8,e^a=e^46,c^b=c^12,d^b=d^122024 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31772, 29);