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C2×D5133 #35206602

order20532
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD10266
direct productC2×D5133
unambiguous semidirect product(C2×C3)⋊D1711
unambiguous semidirect product(C2×C29)⋊D177
unambiguous semidirect product(C2×C59)⋊D87

Splittings

Fitting, socleC2×C3×C29×C59 ⋊ C2
derived, HallC3×C29×C59 ⋊ C22
HallC29×C59 ⋊ C2×D3
HallC3×C59 ⋊ C2×D29
HallC3×C29 ⋊ C2×D59
SylowC59 ⋊ C2×D87
SylowC29 ⋊ C2×D177
SylowC3 ⋊ C2×D1711

Subgroups

subgroupG/H
center, hypercenterC2D5133
commutator, cosocle, hypocenterC3×C29×C59C22
FrattiniC1G
Fitting, socleC2×C3×C29×C59C2
LCSG ▷ C3×C29×C59
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 93
transitive degreeμt(G) = 10266

A minimal faithful permutation representation — 2 generators on 93 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)(35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(4,5)(7,34)(8,33)(9,32)(10,31)(11,30)(12,29)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)(36,93)(37,92)(38,91)(39,90)(40,89)(41,88)(42,87)(43,86)(44,85)(45,84)(46,83)(47,82)(48,81)(49,80)(50,79)(51,78)(52,77)(53,76)(54,75)(55,74)(56,73)(57,72)(58,71)(59,70)(60,69)(61,68)(62,67)(63,66)(64,65)

Conjugacy classes & character table

5136 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD20532, C2×D15399
maximal normal subgroup ofD20532
maximal quotient ofDic10266, D20532, C2×D15399

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20532, 38);