Finite Group DatabasebetaFinite Group Databasebeta| order | 34476 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C132×C17 ⋊ C3×C4 |
| Hall | #26040095 ⋊ C3 |
| Hall | C17×#92788 ⋊ C4 |
| Hall | #92788 ⋊ Dic17 |
| Sylow | C132 ⋊ C3×Dic17 |
| Sylow | C17 ⋊ #14523128 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C17⋊#11759815 |
| commutator, hypocenter | C132×C17 | C3×C4 |
| Fitting, socle, cosocle | C2×C132×C17 | C2×C3 |
| prime radical | C2×C17×#92788 | C2 |
| LCS | G ▷ C132×C17 | |
| UCS | C1 ◁ C2 | |
192 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11492 |
Polycyclic presentation:
2,3,13^2,17,2|a^2=f,c^a=c^12,d^a=d^12,e^a=e^16,c^b=c^3,d^b=d^31012 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34476, 58);