Finite Group Databasebeta

← Group #10714489

Character table — Group #10714489

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888812121212121212121616161616161616161616162424242448484848
order1244222344468888121266688121212242424242466881212242424242424161616161616161644441212121212121212161616162488
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1
χ9222222222222-2-2-2-222222-2-2222-2-2-2-22222-2-222-2-2-2-2-2-20000000000000000000000000000
χ10222222222222-2-2-2-222222-2-2222-2-2-2-2-2-2-2-222-2-2-2-222220000000000000000000000000000
χ112222222-1222-12222-1-1-1-1-122-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-100000000
χ122222222-1222-12222-1-1-1-1-122-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-100000000-2-2-2-21111111100000000
χ132222222-1222-12222-1-1-1-1-122-1-1-1-1-1-1-1-2-211-2-211-1-111110000000022-2-2-1-1-1-1111100000000
χ142222222-1222-12222-1-1-1-1-122-1-1-1-1-1-1-1-2-211-2-211-1-1111100000000-2-2221111-1-1-1-100000000
χ152222222-1222-1-2-2-2-2-1-1-1-1-1-2-2-1-1-1111122-1-1-2-2-1-1111111000000000000−i3−i3i3i3−i3−i3i3i300000000
χ162222222-1222-1-2-2-2-2-1-1-1-1-1-2-2-1-1-1111122-1-1-2-2-1-1111111000000000000i3i3−i3−i3i3i3−i3−i300000000
χ172222222-1222-1-2-2-2-2-1-1-1-1-1-2-2-1-1-11111-2-211221111-1-1-1-1000000000000−i3−i3i3i3i3i3−i3−i300000000
χ182222222-1222-1-2-2-2-2-1-1-1-1-1-2-2-1-1-11111-2-211221111-1-1-1-1000000000000i3i3−i3−i3−i3−i3i3i300000000
χ1922222-2-22-22-222222222-2-2-2-2-2-22222200000000-2-20000000000002i−2i002i−2i2i−2i000000000000
χ2022222-2-22-22-222222222-2-2-2-2-2-22222200000000-2-2000000000000−2i2i00−2i2i−2i2i000000000000
χ2122222-2-22-22-22-2-2-2-2222-2-222-2-22-2-2-2-20000000022000000000000002i−2i00002i−2i2i−2i00000000
χ2222222-2-22-22-22-2-2-2-2222-2-222-2-22-2-2-2-2000000002200000000000000−2i2i0000−2i2i−2i2i00000000
χ2322222-2-2-1-22-2-12222-1-1-111-2-211-1-1-1-1-100−i3i300−i3i311−i3−i3i3i3000000002i−2i00−ii−ii3−3−3300000000
χ2422222-2-2-1-22-2-12222-1-1-111-2-211-1-1-1-1-100−i3i300−i3i311−i3−i3i3i300000000−2i2i00i−ii−i−333−300000000
χ2522222-2-2-1-22-2-12222-1-1-111-2-211-1-1-1-1-100i3−i300i3−i311i3i3−i3−i3000000002i−2i00−ii−ii−333−300000000
χ2622222-2-2-1-22-2-12222-1-1-111-2-211-1-1-1-1-100i3−i300i3−i311i3i3−i3−i300000000−2i2i00i−ii−i3−3−3300000000
χ2722222-2-2-1-22-2-1-2-2-2-2-1-1-1112211-1111100−i3i300−i3i3-1-1i3i3−i3−i300000000002i−2i3−3−33−ii−ii00000000
χ2822222-2-2-1-22-2-1-2-2-2-2-1-1-1112211-1111100−i3i300−i3i3-1-1i3i3−i3−i30000000000−2i2i−333−3i−ii−i00000000
χ2922222-2-2-1-22-2-1-2-2-2-2-1-1-1112211-1111100i3−i300i3−i3-1-1−i3−i3i3i300000000002i−2i−333−3−ii−ii00000000
χ3022222-2-2-1-22-2-1-2-2-2-2-1-1-1112211-1111100i3−i300i3−i3-1-1−i3−i3i3i30000000000−2i2i3−3−33i−ii−i00000000
χ312222-22-222-2-22000022-22-2002-2-2000000002i−2i00002i−2i2i−2i2222−2−2−2−2000000000000−i2−i2i2i20000
χ322222-22-222-2-22000022-22-2002-2-2000000002i−2i00002i−2i2i−2i−2−2−2−22222000000000000i2i2−i2−i20000
χ332222-22-222-2-22000022-22-2002-2-200000000−2i2i0000−2i2i−2i2i2222−2−2−2−2000000000000i2i2−i2−i20000
χ342222-22-222-2-22000022-22-2002-2-200000000−2i2i0000−2i2i−2i2i−2−2−2−22222000000000000−i2−i2i2i20000
χ3522-2-22-2-222-2220000-2-22-2-20022-200002-22200-2-2000000−i2−i2i2i2−i2−i2i2i2000000000000−i2i2−i2i20000
χ3622-2-22-2-222-2220000-2-22-2-20022-200002-22200-2-2000000i2i2−i2−i2i2i2−i2−i2000000000000i2−i2i2−i20000
χ3722-2-22-2-222-2220000-2-22-2-20022-20000-22-2-20022000000−i2−i2i2i2−i2−i2i2i2000000000000i2−i2i2−i20000
χ3822-2-22-2-222-2220000-2-22-2-20022-20000-22-2-20022000000i2i2−i2−i2i2i2−i2−i2000000000000−i2i2−i2i20000
χ3922-2-2-22-22-222222-2-2-2-2-22-2-22-22222-2-2000000002-200000000000000000000000000002-200
χ4022-2-2-22-22-222222-2-2-2-2-22-2-22-22222-2-2000000002-20000000000000000000000000000-2200
χ4122-2-2-22-22-2222-2-222-2-2-22-22-2-222-2-22200000000-220000000000000000000000000000002-2
χ4222-2-2-22-22-2222-2-222-2-2-22-22-2-222-2-22200000000-22000000000000000000000000000000-22
χ4322-2-2-2-22222-2222-2-2-2-2-2-222-22-2222-2-200000000-2200002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ4422-2-2-2-22222-2222-2-2-2-2-2-222-22-2222-2-200000000-220000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ4522-2-2-2-22222-22-2-222-2-2-2-22-222-22-2-222000000002-20000000000000000000000002-2-220000
χ4622-2-2-2-22222-22-2-222-2-2-2-22-222-22-2-222000000002-2000000000000000000000000-222-20000
χ474444-44-4-24-4-4-20000-2-22-2200-222000000004i−4i0000−2i2i−2i2i0000000000000000000000000000
χ484444-44-4-24-4-4-20000-2-22-2200-22200000000−4i4i00002i−2i2i−2i0000000000000000000000000000
χ494444-4-444-4-444000044-4-4400-44-40000000000000000000000000000000000000000000000
χ504444-4-44-2-4-44-20000-2-222-2002-220000000000000023−23−23230000000000000000000000000000
χ514444-4-44-2-4-44-20000-2-222-2002-2200000000000000−232323−230000000000000000000000000000
χ5244-4-44444-4-4-440000-4-444400-4-4-40000000000000000000000000000000000000000000000
χ5344-4-4444-2-4-4-4-2000022-2-2-200222000000−2i32i3002i3−2i30000000000000000000000000000000000
χ5444-4-4444-2-4-4-4-2000022-2-2-2002220000002i3−2i300−2i32i30000000000000000000000000000000000
χ5544-4-44-4-4-24-44-2000022-22200-2-2200004-4-2-200220000000000000000000000000000000000
χ5644-4-44-4-4-24-44-2000022-22200-2-220000-442200-2-20000000000000000000000000000000000
χ5744-4-4-44-4-2-444-244-4-4222-22-442-2-2-2-22200000000-2200000000000000000000000000000000
χ5844-4-4-44-4-2-444-2-4-444222-224-42-2-222-2-2000000002-200000000000000000000000000000000
χ5944-4-4-4-44-244-4-244-4-42222-24-4-22-2-2-222000000002-200000000000000000000000000000000
χ6044-4-4-4-44-244-4-2-4-4442222-2-44-22-222-2-200000000-2200000000000000000000000000000000
χ614-44i−4i0004000-422−22−2i22i24i−4i0000000022−22−2i22i200000000000000ζ11−ζ13−ζ25−ζ29−ζ31−ζ41+ζ43−ζ47−ζ11+ζ13+ζ25+ζ29+ζ31+ζ41−ζ43+ζ47ζ11−ζ13+ζ25−ζ29+ζ31+ζ41+ζ43+ζ47−ζ11+ζ13−ζ25+ζ29−ζ31−ζ41−ζ43−ζ47ζ11+ζ13+ζ25+ζ29−ζ31+ζ41+ζ43−ζ47−ζ11−ζ13−ζ25−ζ29+ζ31−ζ41−ζ43+ζ47ζ11+ζ13−ζ25+ζ29+ζ31−ζ41+ζ43+ζ47−ζ11−ζ13+ζ25−ζ29−ζ31+ζ41−ζ43−ζ4700000000000000000000
χ624-44i−4i0004000-422−22−2i22i24i−4i0000000022−22−2i22i200000000000000−ζ11+ζ13+ζ25+ζ29+ζ31+ζ41−ζ43+ζ47ζ11−ζ13−ζ25−ζ29−ζ31−ζ41+ζ43−ζ47−ζ11+ζ13−ζ25+ζ29−ζ31−ζ41−ζ43−ζ47ζ11−ζ13+ζ25−ζ29+ζ31+ζ41+ζ43+ζ47−ζ11−ζ13−ζ25−ζ29+ζ31−ζ41−ζ43+ζ47ζ11+ζ13+ζ25+ζ29−ζ31+ζ41+ζ43−ζ47−ζ11−ζ13+ζ25−ζ29−ζ31+ζ41−ζ43−ζ47ζ11+ζ13−ζ25+ζ29+ζ31−ζ41+ζ43+ζ4700000000000000000000
χ634-44i−4i0004000-4−22222i2−2i24i−4i00000000−22222i2−2i200000000000000ζ11+ζ13−ζ25+ζ29+ζ31−ζ41+ζ43+ζ47−ζ11−ζ13+ζ25−ζ29−ζ31+ζ41−ζ43−ζ47−ζ11−ζ13−ζ25−ζ29+ζ31−ζ41−ζ43+ζ47ζ11+ζ13+ζ25+ζ29−ζ31+ζ41+ζ43−ζ47ζ11−ζ13+ζ25−ζ29+ζ31+ζ41+ζ43+ζ47−ζ11+ζ13−ζ25+ζ29−ζ31−ζ41−ζ43−ζ47−ζ11+ζ13+ζ25+ζ29+ζ31+ζ41−ζ43+ζ47ζ11−ζ13−ζ25−ζ29−ζ31−ζ41+ζ43−ζ4700000000000000000000
χ644-44i−4i0004000-4−22222i2−2i24i−4i00000000−22222i2−2i200000000000000−ζ11−ζ13+ζ25−ζ29−ζ31+ζ41−ζ43−ζ47ζ11+ζ13−ζ25+ζ29+ζ31−ζ41+ζ43+ζ47ζ11+ζ13+ζ25+ζ29−ζ31+ζ41+ζ43−ζ47−ζ11−ζ13−ζ25−ζ29+ζ31−ζ41−ζ43+ζ47−ζ11+ζ13−ζ25+ζ29−ζ31−ζ41−ζ43−ζ47ζ11−ζ13+ζ25−ζ29+ζ31+ζ41+ζ43+ζ47ζ11−ζ13−ζ25−ζ29−ζ31−ζ41+ζ43−ζ47−ζ11+ζ13+ζ25+ζ29+ζ31+ζ41−ζ43+ζ4700000000000000000000
χ654-4−4i4i0004000-422−222i2−2i2−4i4i0000000022−222i2−2i200000000000000ζ11−ζ13+ζ25−ζ29+ζ31+ζ41+ζ43+ζ47−ζ11+ζ13−ζ25+ζ29−ζ31−ζ41−ζ43−ζ47ζ11−ζ13−ζ25−ζ29−ζ31−ζ41+ζ43−ζ47−ζ11+ζ13+ζ25+ζ29+ζ31+ζ41−ζ43+ζ47−ζ11−ζ13+ζ25−ζ29−ζ31+ζ41−ζ43−ζ47ζ11+ζ13−ζ25+ζ29+ζ31−ζ41+ζ43+ζ47−ζ11−ζ13−ζ25−ζ29+ζ31−ζ41−ζ43+ζ47ζ11+ζ13+ζ25+ζ29−ζ31+ζ41+ζ43−ζ4700000000000000000000
χ664-4−4i4i0004000-422−222i2−2i2−4i4i0000000022−222i2−2i200000000000000−ζ11+ζ13−ζ25+ζ29−ζ31−ζ41−ζ43−ζ47ζ11−ζ13+ζ25−ζ29+ζ31+ζ41+ζ43+ζ47−ζ11+ζ13+ζ25+ζ29+ζ31+ζ41−ζ43+ζ47ζ11−ζ13−ζ25−ζ29−ζ31−ζ41+ζ43−ζ47ζ11+ζ13−ζ25+ζ29+ζ31−ζ41+ζ43+ζ47−ζ11−ζ13+ζ25−ζ29−ζ31+ζ41−ζ43−ζ47ζ11+ζ13+ζ25+ζ29−ζ31+ζ41+ζ43−ζ47−ζ11−ζ13−ζ25−ζ29+ζ31−ζ41−ζ43+ζ4700000000000000000000
χ674-4−4i4i0004000-4−2222−2i22i2−4i4i00000000−2222−2i22i200000000000000ζ11+ζ13+ζ25+ζ29−ζ31+ζ41+ζ43−ζ47−ζ11−ζ13−ζ25−ζ29+ζ31−ζ41−ζ43+ζ47−ζ11−ζ13+ζ25−ζ29−ζ31+ζ41−ζ43−ζ47ζ11+ζ13−ζ25+ζ29+ζ31−ζ41+ζ43+ζ47−ζ11+ζ13+ζ25+ζ29+ζ31+ζ41−ζ43+ζ47ζ11−ζ13−ζ25−ζ29−ζ31−ζ41+ζ43−ζ47ζ11−ζ13+ζ25−ζ29+ζ31+ζ41+ζ43+ζ47−ζ11+ζ13−ζ25+ζ29−ζ31−ζ41−ζ43−ζ4700000000000000000000
χ684-4−4i4i0004000-4−2222−2i22i2−4i4i00000000−2222−2i22i200000000000000−ζ11−ζ13−ζ25−ζ29+ζ31−ζ41−ζ43+ζ47ζ11+ζ13+ζ25+ζ29−ζ31+ζ41+ζ43−ζ47ζ11+ζ13−ζ25+ζ29+ζ31−ζ41+ζ43+ζ47−ζ11−ζ13+ζ25−ζ29−ζ31+ζ41−ζ43−ζ47ζ11−ζ13−ζ25−ζ29−ζ31−ζ41+ζ43−ζ47−ζ11+ζ13+ζ25+ζ29+ζ31+ζ41−ζ43+ζ47−ζ11+ζ13−ζ25+ζ29−ζ31−ζ41−ζ43−ζ47ζ11−ζ13+ζ25−ζ29+ζ31+ζ41+ζ43+ζ4700000000000000000000
χ698-88i−8i000-4000442−42−4i24i2−4i4i00000000−22222i2−2i2000000000000000000000000000000000000000000
χ708-88i−8i000-40004−42424i2−4i2−4i4i0000000022−22−2i22i2000000000000000000000000000000000000000000
χ718-8−8i8i000-4000442−424i2−4i24i−4i00000000−2222−2i22i2000000000000000000000000000000000000000000
χ728-8−8i8i000-40004−4242−4i24i24i−4i0000000022−222i2−2i2000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.