Finite Group DatabasebetaFinite Group Databasebeta| order | 32092 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C71⋊#90673 |
| Fitting, socle, derived, Hall | C71×C113 ⋊ C4 |
| Sylow | C113 ⋊ Dic71 |
| Sylow | C71 ⋊ #90673 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C71×C113 | C4 |
| prime radical, cosocle | C71×D113 | C2 |
| LCS | G ▷ C71×C113 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8023 |
Polycyclic presentation:
2^2,71,113|a^2=b,c^a=c^70,d^a=d^15,d^b=d^1122062 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32092, 7);