Finite Group DatabasebetaFinite Group Databasebeta| order | 34476 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C17×#92789 ⋊ C4 |
| Hall | C132×C17 ⋊ Dic3 |
| Hall | #92789 ⋊ Dic17 |
| Sylow | C132 ⋊ Dic51 |
| Sylow | C17 ⋊ #14523126 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C17⋊#11759813 |
| commutator, hypocenter | C17×#92789 | C4 |
| Fitting, socle | C2×C132×C17 | D3 |
| prime radical, cosocle | C2×C17×#92789 | C2 |
| LCS | G ▷ C17×#92789 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 884 |
Polycyclic presentation:
2,3,17,13^2,2|a^2=f,b^a=b^2,c^a=c^16,d^a=d^3e^8,e^a=d^12e^10,d^b=d^9e^5,e^b=e^31042 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34476, 72);