Finite Group DatabasebetaFinite Group Databasebeta| order | 34180 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C5×C1709 ⋊ C4 |
| Sylow | C1709 ⋊ AGL(1,𝔽5) |
| Sylow | C5 ⋊ #20292020 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C1709 | C4 |
| prime radical, cosocle | D8545 | C2 |
| LCS | G ▷ C5×C1709 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8545 |
Polycyclic presentation:
2^2,5,1709|a^2=b,c^a=c^2,d^a=d^390,c^b=c^4,d^b=d^17082140 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34180, 9);