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C2×D13113 #72289586

order52452
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD26226
direct productC2×D13113

Splittings

FittingC2×C9×C31×C47 ⋊ C2
derived, HallC9×C31×C47 ⋊ C22
HallC31×C47 ⋊ C2×D9
HallC9×C47 ⋊ C2×D31
HallC9×C31 ⋊ C2×D47
SylowC47 ⋊ C2×D279
SylowC31 ⋊ C2×D423
SylowC9 ⋊ C2×D1457

Subgroups

subgroupG/H
center, hypercenterC2D13113
commutator, cosocle, hypocenterC9×C31×C47C22
FrattiniC3C2×D4371
FittingC2×C9×C31×C47C2
socleC2×C3×C31×C47D3
LCSG ▷ C9×C31×C47
UCSC1 ◁ C2

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 89
transitive degreeμt(G) = 26226

A minimal faithful permutation representation — 2 generators on 89 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);(4,11)(5,10)(6,9)(7,8)(13,42)(14,41)(15,40)(16,39)(17,38)(18,37)(19,36)(20,35)(21,34)(22,33)(23,32)(24,31)(25,30)(26,29)(27,28)(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

13116 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)(43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89), (4,11)(5,10)(6,9)(7,8)(13,42)(14,41)(15,40)(16,39)(17,38)(18,37)(19,36)(20,35)(21,34)(22,33)(23,32)(24,31)(25,30)(26,29)(27,28)(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));