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C2×D4565 #32912437

order18260
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD9130
direct productC2×D4565
unambiguous semidirect product(C2×C5)⋊D913
unambiguous semidirect product(C2×C11)⋊D415
unambiguous semidirect product(C2×C83)⋊D55

Splittings

Fitting, socleC2×C5×C11×C83 ⋊ C2
derived, HallC5×C11×C83 ⋊ C22
HallC11×C83 ⋊ C2×D5
HallC5×C83 ⋊ C2×D11
SylowC83 ⋊ C2×D55
HallC5×C11 ⋊ C2×D83
SylowC11 ⋊ C2×D415
SylowC5 ⋊ C2×D913

Subgroups

subgroupG/H
center, hypercenterC2D4565
commutator, cosocle, hypocenterC5×C11×C83C22
FrattiniC1G
Fitting, socleC2×C5×C11×C83C2
LCSG ▷ C5×C11×C83
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 101
transitive degreeμt(G) = 9130

A minimal faithful permutation representation — 2 generators on 101 points:

(1,2)(3,4,5,6,7)(8,9,10,11,12,13,14,15,16,17,18)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101);(4,7)(5,6)(9,18)(10,17)(11,16)(12,15)(13,14)(20,101)(21,100)(22,99)(23,98)(24,97)(25,96)(26,95)(27,94)(28,93)(29,92)(30,91)(31,90)(32,89)(33,88)(34,87)(35,86)(36,85)(37,84)(38,83)(39,82)(40,81)(41,80)(42,79)(43,78)(44,77)(45,76)(46,75)(47,74)(48,73)(49,72)(50,71)(51,70)(52,69)(53,68)(54,67)(55,66)(56,65)(57,64)(58,63)(59,62)(60,61)

Conjugacy classes & character table

4568 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD18260, C2×D13695
maximal normal subgroup ofD18260
maximal quotient ofDic9130, D18260, C2×D13695

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18260, 30);