Finite Group DatabasebetaFinite Group Databasebeta| order | 34164 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C13×C73 ⋊ C4×C9 |
| Hall | #22555440 ⋊ C4 |
| Hall | #16838293 ⋊ C9 |
| Sylow | C73 ⋊ #261⋊C9 |
| Sylow | C13 ⋊ #14581484 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C73 | C4×C9 |
| prime radical, cosocle | D13×C73⋊C3 | C2×C3 |
| LCS | G ▷ C13×C73 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 949 |
Polycyclic presentation:
2,3,2,3,13,73|a^2=c,b^3=d,e^a=e^5,f^a=f^72,e^b=e^3,f^b=f^4,e^c=e^12,f^d=f^6471 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34164, 168);