Finite Group DatabasebetaFinite Group Databasebeta| order | 34476 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C132×C17 ⋊ C3×C4 |
| Hall | #26040106 ⋊ C3 |
| Hall | C13×C17×C13⋊C3 ⋊ C4 |
| Hall | C13×C13⋊C3 ⋊ #595 |
| Sylow | C132 ⋊ C3×#595 |
| Sylow | C17 ⋊ #14523150 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C132×C17 | C3×C4 |
| prime radical | C17⋊((C13⋊C3)⋊D13) | C2 |
| cosocle | C13⋊D221 | C2×C3 |
| LCS | G ▷ C132×C17 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 663 |
Polycyclic presentation:
2,3,2,13^2,17|a^2=c,d^a=d^5,e^a=e^5,f^a=f^4,d^b=d^3,d^c=d^12,e^c=e^12,f^c=f^16398 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34476, 115);