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C2×D13481 #72290293

order53924
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD26962
direct productC2×D13481

Splittings

Fitting, socleC2×C13×C17×C61 ⋊ C2
derived, HallC13×C17×C61 ⋊ C22
HallC17×C61 ⋊ C2×D13
HallC13×C61 ⋊ C2×D17
HallC13×C17 ⋊ C2×D61
SylowC61 ⋊ C2×D221
SylowC17 ⋊ C2×D793
SylowC13 ⋊ C2×D1037

Subgroups

subgroupG/H
center, hypercenterC2D13481
commutator, cosocle, hypocenterC13×C17×C61C22
FrattiniC1G
Fitting, socleC2×C13×C17×C61C2
LCSG ▷ C13×C17×C61
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 93
transitive degreeμt(G) = 26962

A minimal faithful permutation representation — 2 generators on 93 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);(4,15)(5,14)(6,13)(7,12)(8,11)(9,10)(17,32)(18,31)(19,30)(20,29)(21,28)(22,27)(23,26)(24,25)(34,93)(35,92)(36,91)(37,90)(38,89)(39,88)(40,87)(41,86)(42,85)(43,84)(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

13484 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)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93), (4,15)(5,14)(6,13)(7,12)(8,11)(9,10)(17,32)(18,31)(19,30)(20,29)(21,28)(22,27)(23,26)(24,25)(34,93)(35,92)(36,91)(37,90)(38,89)(39,88)(40,87)(41,86)(42,85)(43,84)(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));