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C2×D16133 #72301992

order64532
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD32266
direct productC2×D16133

Splittings

Fitting, socleC2×C13×C17×C73 ⋊ C2
derived, HallC13×C17×C73 ⋊ C22
HallC17×C73 ⋊ C2×D13
HallC13×C73 ⋊ C2×D17
HallC13×C17 ⋊ C2×D73
SylowC73 ⋊ C2×D221
SylowC17 ⋊ C2×D949
SylowC13 ⋊ C2×D1241

Subgroups

subgroupG/H
center, hypercenterC2D16133
commutator, cosocle, hypocenterC13×C17×C73C22
FrattiniC1G
Fitting, socleC2×C13×C17×C73C2
LCSG ▷ C13×C17×C73
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 105
transitive degreeμt(G) = 32266

A minimal faithful permutation representation — 2 generators on 105 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);(4,15)(5,14)(6,13)(7,12)(8,11)(9,10)(17,32)(18,31)(19,30)(20,29)(21,28)(22,27)(23,26)(24,25)(34,105)(35,104)(36,103)(37,102)(38,101)(39,100)(40,99)(41,98)(42,97)(43,96)(44,95)(45,94)(46,93)(47,92)(48,91)(49,90)(50,89)(51,88)(52,87)(53,86)(54,85)(55,84)(56,83)(57,82)(58,81)(59,80)(60,79)(61,78)(62,77)(63,76)(64,75)(65,74)(66,73)(67,72)(68,71)(69,70)

Conjugacy classes & character table

16136 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((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), (4,15)(5,14)(6,13)(7,12)(8,11)(9,10)(17,32)(18,31)(19,30)(20,29)(21,28)(22,27)(23,26)(24,25)(34,105)(35,104)(36,103)(37,102)(38,101)(39,100)(40,99)(41,98)(42,97)(43,96)(44,95)(45,94)(46,93)(47,92)(48,91)(49,90)(50,89)(51,88)(52,87)(53,86)(54,85)(55,84)(56,83)(57,82)(58,81)(59,80)(60,79)(61,78)(62,77)(63,76)(64,75)(65,74)(66,73)(67,72)(68,71)(69,70));