Finite Group DatabasebetaFinite Group Databasebeta| order | 34804 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(#90673⋊C7) |
| unambiguous semidirect product | (C11⋊#90673)⋊C7 |
| Fitting, socle, derived, Hall | C11×C113 ⋊ C4×C7 |
| Hall | C11×C113⋊C7 ⋊ C4 |
| Hall | C11⋊#90673 ⋊ C7 |
| Hall | C113⋊C7 ⋊ Dic11 |
| Sylow | C113 ⋊ C7×Dic11 |
| Sylow | C11 ⋊ #90673⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C11×C113 | C4×C7 |
| prime radical | C11×D113⋊C7 | C2 |
| cosocle | C11×D113 | C2×C7 |
| LCS | G ▷ C11×C113 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1243 |
Polycyclic presentation:
2,7,2,11,113|a^2=c,d^a=d^10,e^a=e^15,e^b=e^49,e^c=e^112142 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34804, 15);