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C2×D8723 #46853098

order34892
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD17446
direct productC2×D8723
unambiguous semidirect product(C2×C11)⋊D793
unambiguous semidirect product(C2×C13)⋊D671
unambiguous semidirect product(C2×C61)⋊D143

Splittings

Fitting, socleC2×C11×C13×C61 ⋊ C2
derived, HallC11×C13×C61 ⋊ C22
HallC13×C61 ⋊ C2×D11
HallC11×C61 ⋊ C2×D13
HallC11×C13 ⋊ C2×D61
SylowC61 ⋊ C2×D143
SylowC13 ⋊ C2×D671
SylowC11 ⋊ C2×D793

Subgroups

subgroupG/H
center, hypercenterC2D8723
commutator, cosocle, hypocenterC11×C13×C61C22
FrattiniC1G
Fitting, socleC2×C11×C13×C61C2
LCSG ▷ C11×C13×C61
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 87
transitive degreeμt(G) = 17446

A minimal faithful permutation representation — 2 generators on 87 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);(4,13)(5,12)(6,11)(7,10)(8,9)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)(28,87)(29,86)(30,85)(31,84)(32,83)(33,82)(34,81)(35,80)(36,79)(37,78)(38,77)(39,76)(40,75)(41,74)(42,73)(43,72)(44,71)(45,70)(46,69)(47,68)(48,67)(49,66)(50,65)(51,64)(52,63)(53,62)(54,61)(55,60)(56,59)(57,58)

Conjugacy classes & character table

8726 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34892, 35);