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C2×D7869 #44538400

order31476
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD15738
direct productC2×D7869
unambiguous semidirect product(C2×C3)⋊D2623
unambiguous semidirect product(C2×C43)⋊D183
unambiguous semidirect product(C2×C61)⋊D129

Splittings

Fitting, socleC2×C3×C43×C61 ⋊ C2
derived, HallC3×C43×C61 ⋊ C22
HallC43×C61 ⋊ C2×D3
HallC3×C61 ⋊ C2×D43
HallC3×C43 ⋊ C2×D61
SylowC61 ⋊ C2×D129
SylowC43 ⋊ C2×D183
SylowC3 ⋊ C2×D2623

Subgroups

subgroupG/H
center, hypercenterC2D7869
commutator, cosocle, hypocenterC3×C43×C61C22
FrattiniC1G
Fitting, socleC2×C3×C43×C61C2
LCSG ▷ C3×C43×C61
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 109
transitive degreeμt(G) = 15738

A minimal faithful permutation representation — 2 generators on 109 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)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109);(4,5)(7,48)(8,47)(9,46)(10,45)(11,44)(12,43)(13,42)(14,41)(15,40)(16,39)(17,38)(18,37)(19,36)(20,35)(21,34)(22,33)(23,32)(24,31)(25,30)(26,29)(27,28)(50,109)(51,108)(52,107)(53,106)(54,105)(55,104)(56,103)(57,102)(58,101)(59,100)(60,99)(61,98)(62,97)(63,96)(64,95)(65,94)(66,93)(67,92)(68,91)(69,90)(70,89)(71,88)(72,87)(73,86)(74,85)(75,84)(76,83)(77,82)(78,81)(79,80)

Conjugacy classes & character table

7872 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD31476
maximal normal subgroup ofD31476
maximal quotient ofDic15738, D31476

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31476, 76);