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C2×D3939 #30628771

order15756
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD7878
direct productC2×D3939
unambiguous semidirect product(C2×C3)⋊D1313
unambiguous semidirect product(C2×C13)⋊D303
unambiguous semidirect product(C2×C101)⋊D39

Splittings

Fitting, socleC2×C3×C13×C101 ⋊ C2
derived, HallC3×C13×C101 ⋊ C22
HallC13×C101 ⋊ C2×D3
HallC3×C101 ⋊ C2×D13
SylowC101 ⋊ C2×D39
HallC3×C13 ⋊ C2×D101
SylowC13 ⋊ C2×D303
SylowC3 ⋊ C2×D1313

Subgroups

subgroupG/H
center, hypercenterC2D3939
commutator, cosocle, hypocenterC3×C13×C101C22
FrattiniC1G
Fitting, socleC2×C3×C13×C101C2
LCSG ▷ C3×C13×C101
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 119
transitive degreeμt(G) = 7878

A minimal faithful permutation representation — 2 generators on 119 points:

(1,2)(3,4,5)(6,7,8,9,10,11,12,13,14,15,16,17,18)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119);(4,5)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)(20,119)(21,118)(22,117)(23,116)(24,115)(25,114)(26,113)(27,112)(28,111)(29,110)(30,109)(31,108)(32,107)(33,106)(34,105)(35,104)(36,103)(37,102)(38,101)(39,100)(40,99)(41,98)(42,97)(43,96)(44,95)(45,94)(46,93)(47,92)(48,91)(49,90)(50,89)(51,88)(52,87)(53,86)(54,85)(55,84)(56,83)(57,82)(58,81)(59,80)(60,79)(61,78)(62,77)(63,76)(64,75)(65,74)(66,73)(67,72)(68,71)(69,70)

Conjugacy classes & character table

3942 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD15756
maximal normal subgroup ofD15756
maximal quotient ofDic7878, D15756

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15756, 46);