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C2×D6615 #72235448

order26460
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD13230
direct productC2×D6615

Splittings

FittingC2×C5×C27×C49 ⋊ C2
derived, HallC5×C27×C49 ⋊ C22
HallC27×C49 ⋊ C2×D5
HallC5×C49 ⋊ C2×D27
HallC5×C27 ⋊ C2×D49
SylowC49 ⋊ C2×D135
SylowC27 ⋊ C2×D245
SylowC5 ⋊ C2×D1323

Subgroups

subgroupG/H
center, hypercenterC2D6615
commutator, cosocle, hypocenterC5×C27×C49C22
FrattiniC7×C9C2×D105
FittingC2×C5×C27×C49C2
socleC2×C3×C5×C7D63
LCSG ▷ C5×C27×C49
UCSC1 ◁ C2

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 83
transitive degreeμt(G) = 13230

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);(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)(31,34)(32,33)(36,83)(37,82)(38,81)(39,80)(40,79)(41,78)(42,77)(43,76)(44,75)(45,74)(46,73)(47,72)(48,71)(49,70)(50,69)(51,68)(52,67)(53,66)(54,65)(55,64)(56,63)(57,62)(58,61)(59,60)

Conjugacy classes & character table

6618 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD26460
maximal normal subgroup ofD26460
maximal quotient ofDic13230, D26460

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), (4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)(31,34)(32,33)(36,83)(37,82)(38,81)(39,80)(40,79)(41,78)(42,77)(43,76)(44,75)(45,74)(46,73)(47,72)(48,71)(49,70)(50,69)(51,68)(52,67)(53,66)(54,65)(55,64)(56,63)(57,62)(58,61)(59,60));