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C2×D4731 #34038745

order18924
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD9462
direct productC2×D4731
unambiguous semidirect product(C2×C3)⋊D1577
unambiguous semidirect product(C2×C19)⋊D249
unambiguous semidirect product(C2×C83)⋊D57

Splittings

Fitting, socleC2×C3×C19×C83 ⋊ C2
derived, HallC3×C19×C83 ⋊ C22
HallC19×C83 ⋊ C2×D3
HallC3×C83 ⋊ C2×D19
SylowC83 ⋊ C2×D57
HallC3×C19 ⋊ C2×D83
SylowC19 ⋊ C2×D249
SylowC3 ⋊ C2×D1577

Subgroups

subgroupG/H
center, hypercenterC2D4731
commutator, cosocle, hypocenterC3×C19×C83C22
FrattiniC1G
Fitting, socleC2×C3×C19×C83C2
LCSG ▷ C3×C19×C83
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 107
transitive degreeμt(G) = 9462

A minimal faithful permutation representation — 2 generators on 107 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)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(4,5)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)(26,107)(27,106)(28,105)(29,104)(30,103)(31,102)(32,101)(33,100)(34,99)(35,98)(36,97)(37,96)(38,95)(39,94)(40,93)(41,92)(42,91)(43,90)(44,89)(45,88)(46,87)(47,86)(48,85)(49,84)(50,83)(51,82)(52,81)(53,80)(54,79)(55,78)(56,77)(57,76)(58,75)(59,74)(60,73)(61,72)(62,71)(63,70)(64,69)(65,68)(66,67)

Conjugacy classes & character table

4734 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD18924, C2×D14193
maximal normal subgroup ofD18924
maximal quotient ofDic9462, D18924, C2×D14193

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18924, 28);