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C2×D6519 #39907706

order26076
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD13038
direct productC2×D6519
unambiguous semidirect product(C2×C3)⋊D2173
unambiguous semidirect product(C2×C41)⋊D159
unambiguous semidirect product(C2×C53)⋊D123

Splittings

Fitting, socleC2×C3×C41×C53 ⋊ C2
derived, HallC3×C41×C53 ⋊ C22
HallC41×C53 ⋊ C2×D3
HallC3×C53 ⋊ C2×D41
HallC3×C41 ⋊ C2×D53
SylowC53 ⋊ C2×D123
SylowC41 ⋊ C2×D159
SylowC3 ⋊ C2×D2173

Subgroups

subgroupG/H
center, hypercenterC2D6519
commutator, cosocle, hypocenterC3×C41×C53C22
FrattiniC1G
Fitting, socleC2×C3×C41×C53C2
LCSG ▷ C3×C41×C53
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 99
transitive degreeμt(G) = 13038

A minimal faithful permutation representation — 2 generators on 99 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);(4,5)(7,46)(8,45)(9,44)(10,43)(11,42)(12,41)(13,40)(14,39)(15,38)(16,37)(17,36)(18,35)(19,34)(20,33)(21,32)(22,31)(23,30)(24,29)(25,28)(26,27)(48,99)(49,98)(50,97)(51,96)(52,95)(53,94)(54,93)(55,92)(56,91)(57,90)(58,89)(59,88)(60,87)(61,86)(62,85)(63,84)(64,83)(65,82)(66,81)(67,80)(68,79)(69,78)(70,77)(71,76)(72,75)(73,74)

Conjugacy classes & character table

6522 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD26076
maximal normal subgroup ofD26076
maximal quotient ofDic13038, D26076

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26076, 36);