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C2×D9401 #49178221

order37604
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD18802
direct productC2×D9401
unambiguous semidirect product(C2×C7)⋊D1343
unambiguous semidirect product(C2×C17)⋊D553
unambiguous semidirect product(C2×C79)⋊D119

Splittings

Fitting, socleC2×C7×C17×C79 ⋊ C2
derived, HallC7×C17×C79 ⋊ C22
HallC17×C79 ⋊ C2×D7
HallC7×C79 ⋊ C2×D17
HallC7×C17 ⋊ C2×D79
SylowC79 ⋊ C2×D119
SylowC17 ⋊ C2×D553
SylowC7 ⋊ C2×D1343

Subgroups

subgroupG/H
center, hypercenterC2D9401
commutator, cosocle, hypocenterC7×C17×C79C22
FrattiniC1G
Fitting, socleC2×C7×C17×C79C2
LCSG ▷ C7×C17×C79
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 105
transitive degreeμt(G) = 18802

A minimal faithful permutation representation — 2 generators on 105 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);(4,9)(5,8)(6,7)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)(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

9404 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37604, 27);