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C2×D13091 #72289458

order52364
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD26182
direct productC2×D13091

Splittings

Fitting, socleC2×C13×C19×C53 ⋊ C2
derived, HallC13×C19×C53 ⋊ C22
HallC19×C53 ⋊ C2×D13
HallC13×C53 ⋊ C2×D19
HallC13×C19 ⋊ C2×D53
SylowC53 ⋊ C2×D247
SylowC19 ⋊ C2×D689
SylowC13 ⋊ C2×D1007

Subgroups

subgroupG/H
center, hypercenterC2D13091
commutator, cosocle, hypocenterC13×C19×C53C22
FrattiniC1G
Fitting, socleC2×C13×C19×C53C2
LCSG ▷ C13×C19×C53
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 87
transitive degreeμt(G) = 26182

A minimal faithful permutation representation — 2 generators on 87 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);(4,15)(5,14)(6,13)(7,12)(8,11)(9,10)(17,34)(18,33)(19,32)(20,31)(21,30)(22,29)(23,28)(24,27)(25,26)(36,87)(37,86)(38,85)(39,84)(40,83)(41,82)(42,81)(43,80)(44,79)(45,78)(46,77)(47,76)(48,75)(49,74)(50,73)(51,72)(52,71)(53,70)(54,69)(55,68)(56,67)(57,66)(58,65)(59,64)(60,63)(61,62)

Conjugacy classes & character table

13094 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), (4,15)(5,14)(6,13)(7,12)(8,11)(9,10)(17,34)(18,33)(19,32)(20,31)(21,30)(22,29)(23,28)(24,27)(25,26)(36,87)(37,86)(38,85)(39,84)(40,83)(41,82)(42,81)(43,80)(44,79)(45,78)(46,77)(47,76)(48,75)(49,74)(50,73)(51,72)(52,71)(53,70)(54,69)(55,68)(56,67)(57,66)(58,65)(59,64)(60,63)(61,62));