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C2×D8643 #46829022

order34572
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD17286
direct productC2×D8643
unambiguous semidirect product(C2×C3)⋊D2881
unambiguous semidirect product(C2×C43)⋊D201
unambiguous semidirect product(C2×C67)⋊D129

Splittings

Fitting, socleC2×C3×C43×C67 ⋊ C2
derived, HallC3×C43×C67 ⋊ C22
HallC43×C67 ⋊ C2×D3
HallC3×C67 ⋊ C2×D43
HallC3×C43 ⋊ C2×D67
SylowC67 ⋊ C2×D129
SylowC43 ⋊ C2×D201
SylowC3 ⋊ C2×D2881

Subgroups

subgroupG/H
center, hypercenterC2D8643
commutator, cosocle, hypocenterC3×C43×C67C22
FrattiniC1G
Fitting, socleC2×C3×C43×C67C2
LCSG ▷ C3×C43×C67
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 115
transitive degreeμt(G) = 17286

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

Conjugacy classes & character table

8646 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34572, 64);