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C2×D13975 #72291268

order55900
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD27950
direct productC2×D13975

Splittings

FittingC2×C13×C25×C43 ⋊ C2
derived, HallC13×C25×C43 ⋊ C22
HallC25×C43 ⋊ C2×D13
HallC13×C43 ⋊ C2×D25
HallC13×C25 ⋊ C2×D43
SylowC43 ⋊ C2×D325
SylowC25 ⋊ C2×D559
SylowC13 ⋊ C2×D1075

Subgroups

subgroupG/H
center, hypercenterC2D13975
commutator, cosocle, hypocenterC13×C25×C43C22
FrattiniC5C2×D2795
FittingC2×C13×C25×C43C2
socleC2×C5×C13×C43D5
LCSG ▷ C13×C25×C43
UCSC1 ◁ C2

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 83
transitive degreeμt(G) = 27950

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);(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)(29,40)(30,39)(31,38)(32,37)(33,36)(34,35)(42,83)(43,82)(44,81)(45,80)(46,79)(47,78)(48,77)(49,76)(50,75)(51,74)(52,73)(53,72)(54,71)(55,70)(56,69)(57,68)(58,67)(59,66)(60,65)(61,64)(62,63)

Conjugacy classes & character table

13978 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), (4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)(29,40)(30,39)(31,38)(32,37)(33,36)(34,35)(42,83)(43,82)(44,81)(45,80)(46,79)(47,78)(48,77)(49,76)(50,75)(51,74)(52,73)(53,72)(54,71)(55,70)(56,69)(57,68)(58,67)(59,66)(60,65)(61,64)(62,63));