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Cayley diagram

D41 #739

order82
isoclinismisoclinic class of D41
automorphismAut(G) = AGL(1,𝔽41) (order 1640) · Inn(G) = G · Out(G) = C4×C5
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

dihedralD41
unambiguous semidirect productC41⋊C2

Splittings

Fitting, socle, derived, SylowC41 ⋊ C2

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC41C2
LCSG ▷ C41
UCSC1

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 41
transitive degreeμt(G) = 41

A minimal faithful permutation representation — 2 generators on 41 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41);(2,41)(3,40)(4,39)(5,38)(6,37)(7,36)(8,35)(9,34)(10,33)(11,32)(12,31)(13,30)(14,29)(15,28)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)

Polycyclic presentation:

2,41|b^a=b^40

Conjugacy classes & character table

22 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#4223, C2×D41, C3×D41, …
maximal normal subgroup of#4223, C2×D41, C3×D41, …
maximal quotient ofDic41, C2×D41, C3×D41, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(82, 1);