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C2×D8103 #44569497

order32412
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD16206
direct productC2×D8103
unambiguous semidirect product(C2×C3)⋊D2701
unambiguous semidirect product(C2×C37)⋊D219
unambiguous semidirect product(C2×C73)⋊D111

Splittings

Fitting, socleC2×C3×C37×C73 ⋊ C2
derived, HallC3×C37×C73 ⋊ C22
HallC37×C73 ⋊ C2×D3
HallC3×C73 ⋊ C2×D37
HallC3×C37 ⋊ C2×D73
SylowC73 ⋊ C2×D111
SylowC37 ⋊ C2×D219
SylowC3 ⋊ C2×D2701

Subgroups

subgroupG/H
center, hypercenterC2D8103
commutator, cosocle, hypocenterC3×C37×C73C22
FrattiniC1G
Fitting, socleC2×C3×C37×C73C2
LCSG ▷ C3×C37×C73
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 115
transitive degreeμt(G) = 16206

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)(7,42)(8,41)(9,40)(10,39)(11,38)(12,37)(13,36)(14,35)(15,34)(16,33)(17,32)(18,31)(19,30)(20,29)(21,28)(22,27)(23,26)(24,25)(44,115)(45,114)(46,113)(47,112)(48,111)(49,110)(50,109)(51,108)(52,107)(53,106)(54,105)(55,104)(56,103)(57,102)(58,101)(59,100)(60,99)(61,98)(62,97)(63,96)(64,95)(65,94)(66,93)(67,92)(68,91)(69,90)(70,89)(71,88)(72,87)(73,86)(74,85)(75,84)(76,83)(77,82)(78,81)(79,80)

Conjugacy classes & character table

8106 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD32412
maximal normal subgroup ofD32412
maximal quotient ofDic16206, D32412

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32412, 100);