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C2×D6715 #41001725

order26860
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD13430
direct productC2×D6715
unambiguous semidirect product(C2×C5)⋊D1343
unambiguous semidirect product(C2×C17)⋊D395
unambiguous semidirect product(C2×C79)⋊D85

Splittings

Fitting, socleC2×C5×C17×C79 ⋊ C2
derived, HallC5×C17×C79 ⋊ C22
HallC17×C79 ⋊ C2×D5
HallC5×C79 ⋊ C2×D17
HallC5×C17 ⋊ C2×D79
SylowC79 ⋊ C2×D85
SylowC17 ⋊ C2×D395
SylowC5 ⋊ C2×D1343

Subgroups

subgroupG/H
center, hypercenterC2D6715
commutator, cosocle, hypocenterC5×C17×C79C22
FrattiniC1G
Fitting, socleC2×C5×C17×C79C2
LCSG ▷ C5×C17×C79
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 103
transitive degreeμt(G) = 13430

A minimal faithful permutation representation — 2 generators on 103 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)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103);(4,7)(5,6)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)(26,103)(27,102)(28,101)(29,100)(30,99)(31,98)(32,97)(33,96)(34,95)(35,94)(36,93)(37,92)(38,91)(39,90)(40,89)(41,88)(42,87)(43,86)(44,85)(45,84)(46,83)(47,82)(48,81)(49,80)(50,79)(51,78)(52,77)(53,76)(54,75)(55,74)(56,73)(57,72)(58,71)(59,70)(60,69)(61,68)(62,67)(63,66)(64,65)

Conjugacy classes & character table

6718 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD26860
maximal normal subgroup ofD26860
maximal quotient ofDic13430, D26860

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26860, 35);