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Cayley diagram

C2×D47 #4422

order188
isoclinismisoclinic class of D47
automorphismAut(G) = C2×AGL(1,𝔽47) (order 4324) · Inn(G) = D47 · Out(G) = C2×C23
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD94
direct productC2×D47
unambiguous semidirect productC47⋊C22
unambiguous semidirect product(C2×C47)⋊C2

Splittings

Fitting, socleC2×C47 ⋊ C2
derived, SylowC47 ⋊ C22

Subgroups

subgroupG/H
center, hypercenterC2D47
commutator, cosocle, hypocenterC47C22
FrattiniC1G
Fitting, socleC2×C47C2
LCSG ▷ C47
UCSC1 ◁ C2

10 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 49
transitive degreeμt(G) = 94

A minimal faithful permutation representation — 2 generators on 49 points:

(1,2)(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49);(4,49)(5,48)(6,47)(7,46)(8,45)(9,44)(10,43)(11,42)(12,41)(13,40)(14,39)(15,38)(16,37)(17,36)(18,35)(19,34)(20,33)(21,32)(22,31)(23,30)(24,29)(25,28)(26,27)

Conjugacy classes & character table

50 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×D47, D188, C22⋊D47, …
maximal normal subgroup ofC4×D47, D188, C22⋊D47, …
maximal quotient ofDic94, C4×D47, D188, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(188, 3);