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C2×D4503 #31824746

order18012
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD9006
direct productC2×D4503
unambiguous semidirect product(C2×C3)⋊D1501
unambiguous semidirect product(C2×C19)⋊D237
unambiguous semidirect product(C2×C79)⋊D57

Splittings

Fitting, socleC2×C3×C19×C79 ⋊ C2
derived, HallC3×C19×C79 ⋊ C22
HallC19×C79 ⋊ C2×D3
HallC3×C79 ⋊ C2×D19
SylowC79 ⋊ C2×D57
HallC3×C19 ⋊ C2×D79
SylowC19 ⋊ C2×D237
SylowC3 ⋊ C2×D1501

Subgroups

subgroupG/H
center, hypercenterC2D4503
commutator, cosocle, hypocenterC3×C19×C79C22
FrattiniC1G
Fitting, socleC2×C3×C19×C79C2
LCSG ▷ C3×C19×C79
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 103
transitive degreeμt(G) = 9006

A minimal faithful permutation representation — 2 generators on 103 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)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103);(4,5)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)(26,103)(27,102)(28,101)(29,100)(30,99)(31,98)(32,97)(33,96)(34,95)(35,94)(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

4506 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD18012, C2×D13509
maximal normal subgroup ofD18012
maximal quotient ofDic9006, D18012, C2×D13509

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18012, 58);