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C2×D4161 #30659161

order16644
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD8322
direct productC2×D4161
unambiguous semidirect product(C2×C3)⋊D1387
unambiguous semidirect product(C2×C19)⋊D219
unambiguous semidirect product(C2×C73)⋊D57

Splittings

Fitting, socleC2×C3×C19×C73 ⋊ C2
derived, HallC3×C19×C73 ⋊ C22
HallC19×C73 ⋊ C2×D3
HallC3×C73 ⋊ C2×D19
SylowC73 ⋊ C2×D57
HallC3×C19 ⋊ C2×D73
SylowC19 ⋊ C2×D219
SylowC3 ⋊ C2×D1387

Subgroups

subgroupG/H
center, hypercenterC2D4161
commutator, cosocle, hypocenterC3×C19×C73C22
FrattiniC1G
Fitting, socleC2×C3×C19×C73C2
LCSG ▷ C3×C19×C73
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 97
transitive degreeμt(G) = 8322

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

Conjugacy classes & character table

4164 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD16644
maximal normal subgroup ofD16644
maximal quotient ofDic8322, D16644

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16644, 70);