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C2×D4015 #30631124

order16060
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD8030
direct productC2×D4015
unambiguous semidirect product(C2×C5)⋊D803
unambiguous semidirect product(C2×C11)⋊D365
unambiguous semidirect product(C2×C73)⋊D55

Splittings

Fitting, socleC2×C5×C11×C73 ⋊ C2
derived, HallC5×C11×C73 ⋊ C22
HallC11×C73 ⋊ C2×D5
HallC5×C73 ⋊ C2×D11
SylowC73 ⋊ C2×D55
HallC5×C11 ⋊ C2×D73
SylowC11 ⋊ C2×D365
SylowC5 ⋊ C2×D803

Subgroups

subgroupG/H
center, hypercenterC2D4015
commutator, cosocle, hypocenterC5×C11×C73C22
FrattiniC1G
Fitting, socleC2×C5×C11×C73C2
LCSG ▷ C5×C11×C73
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 91
transitive degreeμt(G) = 8030

A minimal faithful permutation representation — 2 generators on 91 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);(4,7)(5,6)(9,18)(10,17)(11,16)(12,15)(13,14)(20,91)(21,90)(22,89)(23,88)(24,87)(25,86)(26,85)(27,84)(28,83)(29,82)(30,81)(31,80)(32,79)(33,78)(34,77)(35,76)(36,75)(37,74)(38,73)(39,72)(40,71)(41,70)(42,69)(43,68)(44,67)(45,66)(46,65)(47,64)(48,63)(49,62)(50,61)(51,60)(52,59)(53,58)(54,57)(55,56)

Conjugacy classes & character table

4018 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD16060
maximal normal subgroup ofD16060
maximal quotient ofDic8030, D16060

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16060, 40);