Finite Group DatabasebetaFinite Group Databasebeta| order | 31196 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊#15667778 |
| Fitting, socle, derived, Hall | C11×C709 ⋊ C4 |
| Sylow | C709 ⋊ Dic11 |
| Sylow | C11 ⋊ #15667778 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C11×C709 | C4 |
| prime radical, cosocle | C11×D709 | C2 |
| LCS | G ▷ C11×C709 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7799 |
Polycyclic presentation:
2^2,11,709|a^2=b,c^a=c^10,d^a=d^96,d^b=d^7081961 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31196, 7);