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C2×D6745 #41008709

order26980
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD13490
direct productC2×D6745
unambiguous semidirect product(C2×C5)⋊D1349
unambiguous semidirect product(C2×C19)⋊D355
unambiguous semidirect product(C2×C71)⋊D95

Splittings

Fitting, socleC2×C5×C19×C71 ⋊ C2
derived, HallC5×C19×C71 ⋊ C22
HallC19×C71 ⋊ C2×D5
HallC5×C71 ⋊ C2×D19
HallC5×C19 ⋊ C2×D71
SylowC71 ⋊ C2×D95
SylowC19 ⋊ C2×D355
SylowC5 ⋊ C2×D1349

Subgroups

subgroupG/H
center, hypercenterC2D6745
commutator, cosocle, hypocenterC5×C19×C71C22
FrattiniC1G
Fitting, socleC2×C5×C19×C71C2
LCSG ▷ C5×C19×C71
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 97
transitive degreeμt(G) = 13490

A minimal faithful permutation representation — 2 generators on 97 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);(4,7)(5,6)(9,26)(10,25)(11,24)(12,23)(13,22)(14,21)(15,20)(16,19)(17,18)(28,97)(29,96)(30,95)(31,94)(32,93)(33,92)(34,91)(35,90)(36,89)(37,88)(38,87)(39,86)(40,85)(41,84)(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

6748 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD26980
maximal normal subgroup ofD26980
maximal quotient ofDic13490, D26980

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26980, 36);