Finite Group Databasebeta

← Group #10707207

Character table — Group #10707207

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122222222224444444444444488888888888888161616161616161616161616242424242424242448484848
order122234444446668888121212121212242424241616161624244848484848484848444412121212121212128888161616168888
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-11-111-1-111-1-11111-1-1-1-111-1-1
χ61111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-11-111-1-111-1-1-1-1-1-11111-1-111
χ71111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-11-11-1-111-1-1111111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-1-1-1111111-1-1
χ91111111-1-1-1-111111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1ii−i−iii−i−ii−ii−i
χ101111111-1-1-1-111111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1−i−iii−i−iii−ii−ii
χ111111111-1-1-1-111111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111ii−i−iii−i−i−ii−ii
χ121111111-1-1-1-111111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111−i−iii−i−iiii−ii−i
χ131111111-1-1-1-111111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111111-1-1111-1-1-1-111ii−i−i−i−iiii−i−ii
χ141111111-1-1-1-111111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111111-1-1111-1-1-1-111−i−iiiii−i−i−iii−i
χ151111111-1-1-1-111111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-111-1-1-11111-1-1ii−i−i−i−iii−iii−i
χ161111111-1-1-1-111111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-111-1-1-11111-1-1−i−iiiii−i−ii−i−ii
χ1722222222222222-2-2-2-2222222-2-2-2-20000-2-2000000000000000000002-22-200000000
χ1822222222222222-2-2-2-2222222-2-2-2-20000-2-200000000000000000000-22-2200000000
χ192222222-2-2-2-2222-2-222-2-2-2-222-2-2-2-2000022000000000000000000002i−2i−2i2i00000000
χ202222222-2-2-2-2222-2-222-2-2-2-222-2-2-2-200002200000000000000000000−2i2i2i−2i00000000
χ212222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ222222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ232222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1111111112-22-2-1-111-1-111000000000000
χ242222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-22-2211-1-111-1-1000000000000
χ252222-122-2-2-2-2-1-1-122-2-21111-1-1-1-1-1-122-2-211-1-1-1-1111122-2-2-1-1-1-11111000000000000
χ262222-122-2-2-2-2-1-1-122-2-21111-1-1-1-1-1-122-2-211-1-1-1-11111-2-2221111-1-1-1-1000000000000
χ272222-122-2-2-2-2-1-1-122-2-21111-1-1-1-1-1-1-2-222111111-1-1-1-12-2-22-1-11111-1-1000000000000
χ282222-122-2-2-2-2-1-1-122-2-21111-1-1-1-1-1-1-2-222111111-1-1-1-1-222-211-1-1-1-111000000000000
χ292-2-2222-22i2i−2i−2i-2-222-22i−2i2i2i−2i−2i2-222-2-200002i−2i000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000
χ302-2-2222-22i2i−2i−2i-2-222-22i−2i2i2i−2i−2i2-222-2-200002i−2i0000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000
χ312-2-2222-22i2i−2i−2i-2-22-22−2i2i2i2i−2i−2i2-2-2-2222-22i−2i−2i2i22-2-22i2i−2i−2i000000000000000000000000
χ322-2-2222-22i2i−2i−2i-2-22-22−2i2i2i2i−2i−2i2-2-2-222-22−2i2i−2i2i-2-222−2i−2i2i2i000000000000000000000000
χ332-2-2222-2−2i−2i2i2i-2-222-2−2i2i−2i−2i2i2i2-222-2-20000−2i2i0000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000
χ342-2-2222-2−2i−2i2i2i-2-222-2−2i2i−2i−2i2i2i2-222-2-20000−2i2i000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000
χ352-2-2222-2−2i−2i2i2i-2-22-222i−2i−2i−2i2i2i2-2-2-2222-2−2i2i2i−2i22-2-2−2i−2i2i2i000000000000000000000000
χ362-2-2222-2−2i−2i2i2i-2-22-222i−2i−2i−2i2i2i2-2-2-222-222i−2i2i−2i-2-2222i2i−2i−2i000000000000000000000000
χ372-2-22-12-22i2i−2i−2i11-1-22−2i2i−i−iii-1111-1-12-22i−2ii−i-1-111−i−iii00003−33−3−i3i3−i3i3000000000000
χ382-2-22-12-22i2i−2i−2i11-1-22−2i2i−i−iii-1111-1-12-22i−2ii−i-1-111−i−iii0000−33−33i3−i3i3−i3000000000000
χ392-2-22-12-22i2i−2i−2i11-1-22−2i2i−i−iii-1111-1-1-22−2i2ii−i11-1-1ii−i−i00003−3−33−i3i3i3−i3000000000000
χ402-2-22-12-22i2i−2i−2i11-1-22−2i2i−i−iii-1111-1-1-22−2i2ii−i11-1-1ii−i−i0000−333−3i3−i3−i3i3000000000000
χ412-2-22-12-2−2i−2i2i2i11-1-222i−2iii−i−i-1111-1-12-2−2i2i−ii-1-111ii−i−i00003−33−3i3−i3i3−i3000000000000
χ422-2-22-12-2−2i−2i2i2i11-1-222i−2iii−i−i-1111-1-12-2−2i2i−ii-1-111ii−i−i0000−33−33−i3i3−i3i3000000000000
χ432-2-22-12-2−2i−2i2i2i11-1-222i−2iii−i−i-1111-1-1-222i−2i−ii11-1-1−i−iii00003−3−33i3−i3−i3i3000000000000
χ442-2-22-12-2−2i−2i2i2i11-1-222i−2iii−i−i-1111-1-1-222i−2i−ii11-1-1−i−iii0000−333−3−i3i3i3−i3000000000000
χ4544444-4-44-44-444400004-44-4-4-4000000000000000000000000000000000000000000
χ4644444-4-4-44-444440000-44-44-4-4000000000000000000000000000000000000000000
χ474444-2444444-2-2-2-4-4-4-4-2-2-2-2-2-2222200002200000000000000000000000000000000
χ484444-244-4-4-4-4-2-2-2-4-4442222-2-222220000-2-200000000000000000000000000000000
χ494444-2-4-44-44-4-2-2-20000-22-22220000000000i6−i6i6−i6i6−i6i6−i6000000000000000000000000
χ504444-2-4-44-44-4-2-2-20000-22-22220000000000−i6i6−i6i6−i6i6−i6i6000000000000000000000000
χ514444-2-4-4-44-44-2-2-200002-22-2220000000000i6−i6i6−i6−i6i6−i6i6000000000000000000000000
χ524444-2-4-4-44-44-2-2-200002-22-2220000000000−i6i6−i6i6i6−i6i6−i6000000000000000000000000
χ534-4-444-444i−4i−4i4i-4-4400004i−4i−4i4i-44000000000000000000000000000000000000000000
χ544-4-444-44−4i4i4i−4i-4-440000−4i4i4i−4i-44000000000000000000000000000000000000000000
χ554-4-44-24-44i4i−4i−4i22-24-44i−4i−2i−2i2i2i-22-2-2220000−2i2i00000000000000000000000000000000
χ564-4-44-24-4−4i−4i4i4i22-24-4−4i4i2i2i−2i−2i-22-2-22200002i−2i00000000000000000000000000000000
χ574-4-44-2-444i−4i−4i4i22-20000−2i2i2i−2i2-20000000000i6−i6−i6i6−666−6000000000000000000000000
χ584-4-44-2-444i−4i−4i4i22-20000−2i2i2i−2i2-20000000000−i6i6i6−i66−6−66000000000000000000000000
χ594-4-44-2-44−4i4i4i−4i22-200002i−2i−2i2i2-20000000000i6−i6−i6i66−6−66000000000000000000000000
χ604-4-44-2-44−4i4i4i−4i22-200002i−2i−2i2i2-20000000000−i6i6i6−i6−666−6000000000000000000000000
χ6188-8-880000008-8-80000000000000000000000000000000000000000000000000000
χ6288-8-8-4000000-44400000000002i6−2i62i6−2i600000000000000000000000000000000000000
χ6388-8-8-4000000-4440000000000−2i62i6−2i62i600000000000000000000000000000000000000
χ648-88-88000000-88-80000000000000000000000000000000000000000000000000000
χ658-88-8-40000004-4400000000002i6−2i6−2i62i600000000000000000000000000000000000000
χ668-88-8-40000004-440000000000−2i62i62i6−2i600000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.