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 | C13×#10620321 ⋊ C4 |
| Hall | #16838292 ⋊ C9 |
| Hall | #10620321 ⋊ #261 |
| Sylow | C73 ⋊ C9×#261 |
| Sylow | C13 ⋊ #14581472 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #26015678 |
| commutator, hypocenter | C13×C73 | C4×C9 |
| Fitting, socle | C3×C13×C73 | C3×C4 |
| prime radical, cosocle | C3×D949 | 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^5,e^a=e^46,e^b=e^8,d^c=d^12,e^c=e^72297 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34164, 46);