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C2×D2739 #24926588

order10956
automorphismAut(G) order 8983920
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD5478
direct productC2×D2739
unambiguous semidirect product(C2×C3)⋊D913
unambiguous semidirect product(C2×C11)⋊D249
unambiguous semidirect product(C2×C83)⋊D33

Splittings

Fitting, socleC2×C3×C11×C83 ⋊ C2
derived, HallC3×C11×C83 ⋊ C22
HallC11×C83 ⋊ C2×D3
HallC3×C83 ⋊ C2×D11
SylowC83 ⋊ C2×D33
HallC3×C11 ⋊ C2×D83
SylowC11 ⋊ C2×D249
SylowC3 ⋊ C2×D913

Subgroups

subgroupG/H
center, hypercenterC2D2739
commutator, cosocle, hypocenterC3×C11×C83C22
FrattiniC1G
Fitting, socleC2×C3×C11×C83C2
LCSG ▷ C3×C11×C83
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 99
transitive degreeμt(G) = 5478

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

Conjugacy classes & character table

2742 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×D8217, D3×D2739, C2×C3×D2739, …
maximal normal subgroup ofC2×C3×D2739, D10956
maximal quotient ofC2×D8217, D3×D2739, C2×C3×D2739, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10956, 18);