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Cayley diagram

D43 #758

order86
isoclinismisoclinic class of D43
automorphismAut(G) = AGL(1,𝔽43) (order 1806) · Inn(G) = G · Out(G) = C3×C7
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

dihedralD43
unambiguous semidirect productC43⋊C2

Splittings

Fitting, socle, derived, SylowC43 ⋊ C2

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC43C2
LCSG ▷ C43
UCSC1

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 43
transitive degreeμt(G) = 43

A minimal faithful permutation representation — 2 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43);(2,43)(3,42)(4,41)(5,40)(6,39)(7,38)(8,37)(9,36)(10,35)(11,34)(12,33)(13,32)(14,31)(15,30)(16,29)(17,28)(18,27)(19,26)(20,25)(21,24)(22,23)

Polycyclic presentation:

2,43|b^a=b^42

Conjugacy classes & character table

23 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D43, D43⋊C3, C3×D43, …
maximal normal subgroup ofC2×D43, D43⋊C3, C3×D43, …
maximal quotient ofDic43, C2×D43, C3×D43, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(86, 1);