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C2×D4047 #30633701

order16188
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD8094
direct productC2×D4047
unambiguous semidirect product(C2×C3)⋊D1349
unambiguous semidirect product(C2×C19)⋊D213
unambiguous semidirect product(C2×C71)⋊D57

Splittings

Fitting, socleC2×C3×C19×C71 ⋊ C2
derived, HallC3×C19×C71 ⋊ C22
HallC19×C71 ⋊ C2×D3
HallC3×C71 ⋊ C2×D19
SylowC71 ⋊ C2×D57
HallC3×C19 ⋊ C2×D71
SylowC19 ⋊ C2×D213
SylowC3 ⋊ C2×D1349

Subgroups

subgroupG/H
center, hypercenterC2D4047
commutator, cosocle, hypocenterC3×C19×C71C22
FrattiniC1G
Fitting, socleC2×C3×C19×C71C2
LCSG ▷ C3×C19×C71
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 95
transitive degreeμt(G) = 8094

A minimal faithful permutation representation — 2 generators on 95 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);(4,5)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)(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

4050 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD16188
maximal normal subgroup ofD16188
maximal quotient ofDic8094, D16188

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16188, 28);