Finite Group DatabasebetaFinite Group Databasebeta| order | 31772 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C47⋊#10621721 |
| Fitting, derived, Hall | C47×C169 ⋊ C4 |
| Sylow | C169 ⋊ Dic47 |
| Sylow | C47 ⋊ #10621721 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C47×C169 | C4 |
| Frattini | C13 | C47⋊#261 |
| socle | C13×C47 | #261 |
| prime radical, cosocle | C47×D169 | C2 |
| LCS | G ▷ C47×C169 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7943 |
Polycyclic presentation:
2^2,13,47,13|a^2=b,c^13=e^8,c^a=c^5e,d^a=d^46,e^a=e^5,c^b=c^12e^5,e^b=e^122024 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31772, 7);