Finite Group DatabasebetaFinite Group Databasebeta| order | 34476 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, Hall | C132×C17 ⋊ Dic3 |
| derived, Hall | C17×#92789 ⋊ C4 |
| Hall | #92789 ⋊ #595 |
| Sylow | C132 ⋊ C3⋊#595 |
| Sylow | C17 ⋊ #14523126 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C17×#92789 | C4 |
| Fitting, socle | C132×C17 | Dic3 |
| prime radical, cosocle | D17×#92789 | C2 |
| LCS | G ▷ C17×#92789 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 442 |
Polycyclic presentation:
2^2,3,17,13^2|a^2=b,c^a=c^2,d^a=d^13,e^a=e^9f^2,f^a=e^12f^4,d^b=d^16,e^c=e^3f^11,f^c=f^9334 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34476, 88);