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C2×D8695 #46852016

order34780
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD17390
direct productC2×D8695
unambiguous semidirect product(C2×C5)⋊D1739
unambiguous semidirect product(C2×C37)⋊D235
unambiguous semidirect product(C2×C47)⋊D185

Splittings

Fitting, socleC2×C5×C37×C47 ⋊ C2
derived, HallC5×C37×C47 ⋊ C22
HallC37×C47 ⋊ C2×D5
HallC5×C47 ⋊ C2×D37
HallC5×C37 ⋊ C2×D47
SylowC47 ⋊ C2×D185
SylowC37 ⋊ C2×D235
SylowC5 ⋊ C2×D1739

Subgroups

subgroupG/H
center, hypercenterC2D8695
commutator, cosocle, hypocenterC5×C37×C47C22
FrattiniC1G
Fitting, socleC2×C5×C37×C47C2
LCSG ▷ C5×C37×C47
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 91
transitive degreeμt(G) = 17390

A minimal faithful permutation representation — 2 generators on 91 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);(4,7)(5,6)(9,44)(10,43)(11,42)(12,41)(13,40)(14,39)(15,38)(16,37)(17,36)(18,35)(19,34)(20,33)(21,32)(22,31)(23,30)(24,29)(25,28)(26,27)(46,91)(47,90)(48,89)(49,88)(50,87)(51,86)(52,85)(53,84)(54,83)(55,82)(56,81)(57,80)(58,79)(59,78)(60,77)(61,76)(62,75)(63,74)(64,73)(65,72)(66,71)(67,70)(68,69)

Conjugacy classes & character table

8698 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34780, 35);