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C2×D8555 #46803791

order34220
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD17110
direct productC2×D8555
unambiguous semidirect product(C2×C5)⋊D1711
unambiguous semidirect product(C2×C29)⋊D295
unambiguous semidirect product(C2×C59)⋊D145

Splittings

Fitting, socleC2×C5×C29×C59 ⋊ C2
derived, HallC5×C29×C59 ⋊ C22
HallC29×C59 ⋊ C2×D5
HallC5×C59 ⋊ C2×D29
HallC5×C29 ⋊ C2×D59
SylowC59 ⋊ C2×D145
SylowC29 ⋊ C2×D295
SylowC5 ⋊ C2×D1711

Subgroups

subgroupG/H
center, hypercenterC2D8555
commutator, cosocle, hypocenterC5×C29×C59C22
FrattiniC1G
Fitting, socleC2×C5×C29×C59C2
LCSG ▷ C5×C29×C59
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 95
transitive degreeμt(G) = 17110

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);(4,7)(5,6)(9,36)(10,35)(11,34)(12,33)(13,32)(14,31)(15,30)(16,29)(17,28)(18,27)(19,26)(20,25)(21,24)(22,23)(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

8558 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34220, 46);