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C2×D13671 #72290653

order54684
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD27342
direct productC2×D13671

Splittings

FittingC2×C9×C31×C49 ⋊ C2
derived, HallC9×C31×C49 ⋊ C22
HallC31×C49 ⋊ C2×D9
HallC9×C49 ⋊ C2×D31
HallC9×C31 ⋊ C2×D49
SylowC49 ⋊ C2×D279
SylowC31 ⋊ C2×D441
SylowC9 ⋊ C2×D1519

Subgroups

subgroupG/H
center, hypercenterC2D13671
commutator, cosocle, hypocenterC9×C31×C49C22
FrattiniC3×C7C2×D651
FittingC2×C9×C31×C49C2
socleC2×C3×C7×C31D21
LCSG ▷ C9×C31×C49
UCSC1 ◁ C2

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 91
transitive degreeμt(G) = 27342

A minimal faithful permutation representation — 2 generators on 91 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);(4,11)(5,10)(6,9)(7,8)(13,60)(14,59)(15,58)(16,57)(17,56)(18,55)(19,54)(20,53)(21,52)(22,51)(23,50)(24,49)(25,48)(26,47)(27,46)(28,45)(29,44)(30,43)(31,42)(32,41)(33,40)(34,39)(35,38)(36,37)(62,91)(63,90)(64,89)(65,88)(66,87)(67,86)(68,85)(69,84)(70,83)(71,82)(72,81)(73,80)(74,79)(75,78)(76,77)

Conjugacy classes & character table

13674 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), (4,11)(5,10)(6,9)(7,8)(13,60)(14,59)(15,58)(16,57)(17,56)(18,55)(19,54)(20,53)(21,52)(22,51)(23,50)(24,49)(25,48)(26,47)(27,46)(28,45)(29,44)(30,43)(31,42)(32,41)(33,40)(34,39)(35,38)(36,37)(62,91)(63,90)(64,89)(65,88)(66,87)(67,86)(68,85)(69,84)(70,83)(71,82)(72,81)(73,80)(74,79)(75,78)(76,77));