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C2×D6351 #38761964

order25404
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD12702
direct productC2×D6351
unambiguous semidirect product(C2×C3)⋊D2117
unambiguous semidirect product(C2×C29)⋊D219
unambiguous semidirect product(C2×C73)⋊D87

Splittings

Fitting, socleC2×C3×C29×C73 ⋊ C2
derived, HallC3×C29×C73 ⋊ C22
HallC29×C73 ⋊ C2×D3
HallC3×C73 ⋊ C2×D29
HallC3×C29 ⋊ C2×D73
SylowC73 ⋊ C2×D87
SylowC29 ⋊ C2×D219
SylowC3 ⋊ C2×D2117

Subgroups

subgroupG/H
center, hypercenterC2D6351
commutator, cosocle, hypocenterC3×C29×C73C22
FrattiniC1G
Fitting, socleC2×C3×C29×C73C2
LCSG ▷ C3×C29×C73
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 107
transitive degreeμt(G) = 12702

A minimal faithful permutation representation — 2 generators on 107 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)(35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(4,5)(7,34)(8,33)(9,32)(10,31)(11,30)(12,29)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)(36,107)(37,106)(38,105)(39,104)(40,103)(41,102)(42,101)(43,100)(44,99)(45,98)(46,97)(47,96)(48,95)(49,94)(50,93)(51,92)(52,91)(53,90)(54,89)(55,88)(56,87)(57,86)(58,85)(59,84)(60,83)(61,82)(62,81)(63,80)(64,79)(65,78)(66,77)(67,76)(68,75)(69,74)(70,73)(71,72)

Conjugacy classes & character table

6354 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD25404
maximal normal subgroup ofD25404
maximal quotient ofDic12702, D25404

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25404, 52);