Finite Group DatabasebetaFinite Group Databasebeta| order | 34180 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic8545 |
| derived, Hall | C5×C1709 ⋊ C4 |
| Sylow | C1709 ⋊ Dic5 |
| Sylow | C5 ⋊ Dic1709 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D8545 |
| commutator, hypocenter | C5×C1709 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C5×C1709 | C2 |
| LCS | G ▷ C5×C1709 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 1718 |
| transitive degree | μt(G) = 34180 |
A minimal faithful permutation representation — 2 generators on 1718 points:
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presentation:
2,5,1709,2|a^2=d,b^a=b^4,c^a=c^17088548 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34180, 4);