Finite Group DatabasebetaFinite Group Databasebeta| order | 34164 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C13×C73 ⋊ C4×C9 |
| Hall | C73×C13⋊C9 ⋊ C4 |
| Hall | #16838294 ⋊ C9 |
| Hall | C13⋊C9 ⋊ #64408 |
| Sylow | C73 ⋊ Dic13⋊C9 |
| Sylow | C13 ⋊ C9×#64408 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #26015675 |
| commutator, hypocenter | C13×C73 | C4×C9 |
| Fitting, socle | C3×C13×C73 | C3×C4 |
| prime radical, cosocle | C3×C13×D73 | C2×C3 |
| LCS | G ▷ C13×C73 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8541 |
Polycyclic presentation:
2,3,2,13,73,3|a^2=c,b^3=f,d^a=d^12,e^a=e^27,d^b=d^3,e^c=e^72426 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34164, 43);