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C2×C13×C3⋊D219 #46803023

order34164
automorphism?
homologyAbelianization (H1) = C22×C13 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C13×C3⋊D219
unambiguous semidirect product(C2×C3)⋊(C13×D219)
unambiguous semidirect product(C2×C73)⋊(C13×C3⋊D3)

Splittings

Fitting, socleC2×C32×C13×C73 ⋊ C2
derived, HallC32×C73 ⋊ C22×C13
HallC32×C13×C73 ⋊ C22
HallC13×C73 ⋊ C2×C3⋊D3
HallC32×C13 ⋊ C2×D73
SylowC73 ⋊ C2×C13×C3⋊D3
SylowC32 ⋊ C2×C13×D73

Subgroups

subgroupG/H
center, hypercenterC2×C13C3⋊D219
commutator, cosocle, hypocenterC32×C73C22×C13
FrattiniC1G
Fitting, socleC2×C32×C13×C73C2
LCSG ▷ C32×C73
UCSC1 ◁ C2×C13

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 94
transitive degreeμt(G) = 17082

A minimal faithful permutation representation — 3 generators on 94 points:

(4,5)(7,8)(9,10,11,12,13,14,15,16,17,18,19,20,21)(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);(1,2)(6,7,8)(22,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79,81,83,85,87,89,91,93,94,92,90,88,86,84,82,80,78,76,74,72,70,68,66,64,62,60,58,56,54,52,50,48,46,44,42,40,38,36,34,32,30,28,26,24);(3,4,5)

Conjugacy classes & character table

8580 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34164, 389);