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Cayley diagram

D47 #791

order94
isoclinismisoclinic class of D47
automorphismAut(G) = AGL(1,𝔽47) (order 2162) · Inn(G) = G · Out(G) = C23
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

dihedralD47
unambiguous semidirect productC47⋊C2

Splittings

Fitting, socle, derived, SylowC47 ⋊ C2

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC47C2
LCSG ▷ C47
UCSC1

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 47
transitive degreeμt(G) = 47

A minimal faithful permutation representation — 2 generators on 47 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47);(2,47)(3,46)(4,45)(5,44)(6,43)(7,42)(8,41)(9,40)(10,39)(11,38)(12,37)(13,36)(14,35)(15,34)(16,33)(17,32)(18,31)(19,30)(20,29)(21,28)(22,27)(23,26)(24,25)

Polycyclic presentation:

2,47|b^a=b^46

Conjugacy classes & character table

25 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D47, C3×D47, D141, …
maximal normal subgroup ofC2×D47, C3×D47, C5×D47, …
maximal quotient ofDic47, C2×D47, C3×D47, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(94, 1);