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C2×D13651 #72290620

order54604
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD27302
direct productC2×D13651

Splittings

Fitting, socleC2×C11×C17×C73 ⋊ C2
derived, HallC11×C17×C73 ⋊ C22
HallC17×C73 ⋊ C2×D11
HallC11×C73 ⋊ C2×D17
HallC11×C17 ⋊ C2×D73
SylowC73 ⋊ C2×D187
SylowC17 ⋊ C2×D803
SylowC11 ⋊ C2×D1241

Subgroups

subgroupG/H
center, hypercenterC2D13651
commutator, cosocle, hypocenterC11×C17×C73C22
FrattiniC1G
Fitting, socleC2×C11×C17×C73C2
LCSG ▷ C11×C17×C73
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 103
transitive degreeμt(G) = 27302

A minimal faithful permutation representation — 2 generators on 103 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);(4,13)(5,12)(6,11)(7,10)(8,9)(15,30)(16,29)(17,28)(18,27)(19,26)(20,25)(21,24)(22,23)(32,103)(33,102)(34,101)(35,100)(36,99)(37,98)(38,97)(39,96)(40,95)(41,94)(42,93)(43,92)(44,91)(45,90)(46,89)(47,88)(48,87)(49,86)(50,85)(51,84)(52,83)(53,82)(54,81)(55,80)(56,79)(57,78)(58,77)(59,76)(60,75)(61,74)(62,73)(63,72)(64,71)(65,70)(66,69)(67,68)

Conjugacy classes & character table

13654 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), (4,13)(5,12)(6,11)(7,10)(8,9)(15,30)(16,29)(17,28)(18,27)(19,26)(20,25)(21,24)(22,23)(32,103)(33,102)(34,101)(35,100)(36,99)(37,98)(38,97)(39,96)(40,95)(41,94)(42,93)(43,92)(44,91)(45,90)(46,89)(47,88)(48,87)(49,86)(50,85)(51,84)(52,83)(53,82)(54,81)(55,80)(56,79)(57,78)(58,77)(59,76)(60,75)(61,74)(62,73)(63,72)(64,71)(65,70)(66,69)(67,68));