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C2×D15521 #72298960

order62084
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD31042
direct productC2×D15521

Splittings

Fitting, socleC2×C11×C17×C83 ⋊ C2
derived, HallC11×C17×C83 ⋊ C22
HallC17×C83 ⋊ C2×D11
HallC11×C83 ⋊ C2×D17
HallC11×C17 ⋊ C2×D83
SylowC83 ⋊ C2×D187
SylowC17 ⋊ C2×D913
SylowC11 ⋊ C2×D1411

Subgroups

subgroupG/H
center, hypercenterC2D15521
commutator, cosocle, hypocenterC11×C17×C83C22
FrattiniC1G
Fitting, socleC2×C11×C17×C83C2
LCSG ▷ C11×C17×C83
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 113
transitive degreeμt(G) = 31042

A minimal faithful permutation representation — 2 generators on 113 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);(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)(32,113)(33,112)(34,111)(35,110)(36,109)(37,108)(38,107)(39,106)(40,105)(41,104)(42,103)(43,102)(44,101)(45,100)(46,99)(47,98)(48,97)(49,96)(50,95)(51,94)(52,93)(53,92)(54,91)(55,90)(56,89)(57,88)(58,87)(59,86)(60,85)(61,84)(62,83)(63,82)(64,81)(65,80)(66,79)(67,78)(68,77)(69,76)(70,75)(71,74)(72,73)

Conjugacy classes & character table

15524 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)(31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113), (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)(32,113)(33,112)(34,111)(35,110)(36,109)(37,108)(38,107)(39,106)(40,105)(41,104)(42,103)(43,102)(44,101)(45,100)(46,99)(47,98)(48,97)(49,96)(50,95)(51,94)(52,93)(53,92)(54,91)(55,90)(56,89)(57,88)(58,87)(59,86)(60,85)(61,84)(62,83)(63,82)(64,81)(65,80)(66,79)(67,78)(68,77)(69,76)(70,75)(71,74)(72,73));