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C2×D8437 #46798166

order33748
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD16874
direct productC2×D8437
unambiguous semidirect product(C2×C11)⋊D767
unambiguous semidirect product(C2×C13)⋊D649
unambiguous semidirect product(C2×C59)⋊D143

Splittings

Fitting, socleC2×C11×C13×C59 ⋊ C2
derived, HallC11×C13×C59 ⋊ C22
HallC13×C59 ⋊ C2×D11
HallC11×C59 ⋊ C2×D13
HallC11×C13 ⋊ C2×D59
SylowC59 ⋊ C2×D143
SylowC13 ⋊ C2×D649
SylowC11 ⋊ C2×D767

Subgroups

subgroupG/H
center, hypercenterC2D8437
commutator, cosocle, hypocenterC11×C13×C59C22
FrattiniC1G
Fitting, socleC2×C11×C13×C59C2
LCSG ▷ C11×C13×C59
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 85
transitive degreeμt(G) = 16874

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

Conjugacy classes & character table

8440 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33748, 27);