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 | C13×#11725132 ⋊ C3 |
| Hall | C17×#92788 ⋊ C4 |
| Hall | #92788 ⋊ Dic17 |
| Sylow | C132 ⋊ C3×Dic17 |
| Sylow | C17 ⋊ #14523152 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C132×C17 | C3×C4 |
| prime radical | C17×#11759817 | C2 |
| cosocle | C13×C17×D13 | C2×C3 |
| LCS | G ▷ C132×C17 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 884 |
Polycyclic presentation:
2,3,2,13^2,17|a^2=c,d^a=d^5,f^a=f^16,d^b=d^3,e^b=e^3,d^c=d^12361 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34476, 146);