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C2×D13079 #72289412

order52316
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD26158
direct productC2×D13079

Splittings

Fitting, socleC2×C11×C29×C41 ⋊ C2
derived, HallC11×C29×C41 ⋊ C22
HallC29×C41 ⋊ C2×D11
HallC11×C41 ⋊ C2×D29
HallC11×C29 ⋊ C2×D41
SylowC41 ⋊ C2×D319
SylowC29 ⋊ C2×D451
SylowC11 ⋊ C2×D1189

Subgroups

subgroupG/H
center, hypercenterC2D13079
commutator, cosocle, hypocenterC11×C29×C41C22
FrattiniC1G
Fitting, socleC2×C11×C29×C41C2
LCSG ▷ C11×C29×C41
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 83
transitive degreeμt(G) = 26158

A minimal faithful permutation representation — 2 generators on 83 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);(4,13)(5,12)(6,11)(7,10)(8,9)(15,42)(16,41)(17,40)(18,39)(19,38)(20,37)(21,36)(22,35)(23,34)(24,33)(25,32)(26,31)(27,30)(28,29)(44,83)(45,82)(46,81)(47,80)(48,79)(49,78)(50,77)(51,76)(52,75)(53,74)(54,73)(55,72)(56,71)(57,70)(58,69)(59,68)(60,67)(61,66)(62,65)(63,64)

Conjugacy classes & character table

13082 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((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), (4,13)(5,12)(6,11)(7,10)(8,9)(15,42)(16,41)(17,40)(18,39)(19,38)(20,37)(21,36)(22,35)(23,34)(24,33)(25,32)(26,31)(27,30)(28,29)(44,83)(45,82)(46,81)(47,80)(48,79)(49,78)(50,77)(51,76)(52,75)(53,74)(54,73)(55,72)(56,71)(57,70)(58,69)(59,68)(60,67)(61,66)(62,65)(63,64));