Finite Group Databasebeta

← Group #10691264

Character table — Group #10691264

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881212121216161616161616161616242424242424242424244848
order1222222222366644446666661212121244448888121224242424242424244444441212121212121212444444888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ61111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111111111-1-1
χ911111-1-11-1-1111111-1-11-1-1-11-111-1-1ii−i−iii−i−i1-1iiii−i−i−i−i11-1-11-1ii−i−i11-1-11-1ii−i−iii−i−i1-1
χ1011111-1-11-1-1111111-1-11-1-1-11-111-1-1ii−i−iii−i−i1-1iiii−i−i−i−i-1-1111-1ii−i−i11-1-1-11−i−iii−i−iii-11
χ1111111-1-11-1-1111111-1-11-1-1-11-111-1-1ii−i−i−i−iii1-1−i−i−i−iiiii11-1-1-11ii−i−i-1-1111-1ii−i−i−i−iii-11
χ1211111-1-11-1-1111111-1-11-1-1-11-111-1-1ii−i−i−i−iii1-1−i−i−i−iiiii-1-111-11ii−i−i-1-111-11−i−iiiii−i−i1-1
χ1311111-1-11-1-1111111-1-11-1-1-11-111-1-1−i−iiiii−i−i1-1iiii−i−i−i−i11-1-1-11−i−iii-1-1111-1−i−iiiii−i−i-11
χ1411111-1-11-1-1111111-1-11-1-1-11-111-1-1−i−iiiii−i−i1-1iiii−i−i−i−i-1-111-11−i−iii-1-111-11ii−i−i−i−iii1-1
χ1511111-1-11-1-1111111-1-11-1-1-11-111-1-1−i−iii−i−iii1-1−i−i−i−iiiii11-1-11-1−i−iii11-1-11-1−i−iii−i−iii1-1
χ1611111-1-11-1-1111111-1-11-1-1-11-111-1-1−i−iii−i−iii1-1−i−i−i−iiiii-1-1111-1−i−iii11-1-1-11ii−i−iii−i−i-11
χ1722222222222222-2-2-2-2222222-2-2-2-200000000-2-20000000022220000000000-2-20000000000
χ1822222222222222-2-2-2-2222222-2-2-2-200000000-2-200000000-2-2-2-20000000000220000000000
χ192222222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-1000000000000
χ202222222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1111111110000-2-2-1-1-1-11111000000000000
χ212222222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-10000-2-211111111000000000000
χ222222222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111110000221111-1-1-1-1000000000000
χ2322222-2-22-2-22222-2-2222-2-2-22-2-2-22200000000-220000000022-2-20000000000-220000000000
χ2422222-2-22-2-22222-2-2222-2-2-22-2-2-22200000000-2200000000-2-22200000000002-20000000000
χ2522222-2-22-2-2-1-1-1-122-2-2-1111-11-1-1112i2i−2i−2i2i2i−2i−2i-11−i−i−i−iiiii00002-2−i−iii-1-111000000000000
χ2622222-2-22-2-2-1-1-1-122-2-2-1111-11-1-1112i2i−2i−2i−2i−2i2i2i-11iiii−i−i−i−i0000-22−i−iii11-1-1000000000000
χ2722222-2-22-2-2-1-1-1-122-2-2-1111-11-1-111−2i−2i2i2i2i2i−2i−2i-11−i−i−i−iiiii0000-22ii−i−i11-1-1000000000000
χ2822222-2-22-2-2-1-1-1-122-2-2-1111-11-1-111−2i−2i2i2i−2i−2i2i2i-11iiii−i−i−i−i00002-2ii−i−i-1-111000000000000
χ292222-222-2-2-222222-22-2-222-2-2-222222i−2i2i−2i0000-2-2000000000000002i−2i2i−2i0000000000000000
χ302222-222-2-2-222222-22-2-222-2-2-22222−2i2i−2i2i0000-2-200000000000000−2i2i−2i2i0000000000000000
χ312222-222-2-2-22222-22-22-222-2-2-2-2-2-2-200000000220000000000000000000000002i−2i2i−2i000000
χ322222-222-2-2-22222-22-22-222-2-2-2-2-2-2-20000000022000000000000000000000000−2i2i−2i2i000000
χ332222-222-2-2-2-1-1-1-12-22-21-1-1111-1-1-1-12i−2i2i−2i000011−i3−i3i3i3−i3−i3i3i3000000−ii−ii3−33−3000000000000
χ342222-222-2-2-2-1-1-1-12-22-21-1-1111-1-1-1-12i−2i2i−2i000011i3i3−i3−i3i3i3−i3−i3000000−ii−ii−33−33000000000000
χ352222-222-2-2-2-1-1-1-12-22-21-1-1111-1-1-1-1−2i2i−2i2i000011−i3−i3i3i3−i3−i3i3i3000000i−ii−i−33−33000000000000
χ362222-222-2-2-2-1-1-1-12-22-21-1-1111-1-1-1-1−2i2i−2i2i000011i3i3−i3−i3i3i3−i3−i3000000i−ii−i3−33−3000000000000
χ372222-2-2-2-22222222-2-22-2-2-22-2222-2-22-2-220000-22000000000000002-2-220000000000000000
χ382222-2-2-2-22222222-2-22-2-2-22-2222-2-2-222-20000-2200000000000000-222-20000000000000000
χ392222-2-2-2-2222222-222-2-2-2-22-22-2-222000000002-20000000000000000000000002-2-22000000
χ402222-2-2-2-2222222-222-2-2-2-22-22-2-222000000002-2000000000000000000000000-222-2000000
χ412222-2-2-2-222-1-1-1-12-2-22111-11-1-1-1112-2-2200001-133−3−3−3−333000000-111-1−333−3000000000000
χ422222-2-2-2-222-1-1-1-12-2-22111-11-1-1-1112-2-2200001-1−3−33333−3−3000000-111-13−3−33000000000000
χ432222-2-2-2-222-1-1-1-12-2-22111-11-1-1-111-222-200001-133−3−3−3−3330000001-1-113−3−33000000000000
χ442222-2-2-2-222-1-1-1-12-2-22111-11-1-1-111-222-200001-1−3−33333−3−30000001-1-11−333−3000000000000
χ452-2-2222-2-22-222-2-2000022-2-2-2200000000−i2i2−i2i200−i2i2−i2i2−i2i2−i2i22i−2i2i−2i00000000000000002−22−200
χ462-2-2222-2-22-222-2-2000022-2-2-2200000000−i2i2−i2i200−i2i2−i2i2−i2i2−i2i2−2i2i−2i2i0000000000000000−22−2200
χ472-2-2222-2-22-222-2-2000022-2-2-2200000000i2−i2i2−i200i2−i2i2−i2i2−i2i2−i22i−2i2i−2i0000000000000000−22−2200
χ482-2-2222-2-22-222-2-2000022-2-2-2200000000i2−i2i2−i200i2−i2i2−i2i2−i2i2−i2−2i2i−2i2i00000000000000002−22−200
χ492-2-222-22-2-2222-2-200002-222-2-2000000002−2−22002−22−2−22−222i−2i−2i2i0000000000000000i2−i2−i2i200
χ502-2-222-22-2-2222-2-200002-222-2-2000000002−2−22002−22−2−22−22−2i2i2i−2i0000000000000000−i2i2i2−i200
χ512-2-222-22-2-2222-2-200002-222-2-200000000−222−200−22−222−22−22i−2i−2i2i0000000000000000−i2i2i2−i200
χ522-2-222-22-2-2222-2-200002-222-2-200000000−222−200−22−222−22−2−2i2i2i−2i0000000000000000i2−i2−i2i200
χ534444444444-2-2-2-2-4-4-4-4-2-2-2-2-2-2222200000000220000000000000000000000000000000000
χ5444444-4-44-4-4-2-2-2-2-4-444-2222-2222-2-2000000002-20000000000000000000000000000000000
χ554444-444-4-4-4-2-2-2-2-44-442-2-2222222200000000-2-20000000000000000000000000000000000
χ564444-4-4-4-444-2-2-2-2-444-4222-22-222-2-200000000-220000000000000000000000000000000000
χ574-4-4444-4-44-4-2-2220000-2-2222-200000000−2i22i2−2i22i200i2−i2i2−i2i2−i2i2−i200000000000000000000000000
χ584-4-4444-4-44-4-2-2220000-2-2222-2000000002i2−2i22i2−2i200−i2i2−i2i2−i2i2−i2i200000000000000000000000000
χ594-4-444-44-4-44-2-2220000-22-2-2220000000022−22−222200−22−222−22−200000000000000000000000000
χ604-4-444-44-4-44-2-2220000-22-2-22200000000−222222−22002−22−2−22−2200000000000000000000000000
χ614-4-44-44-44-4444-4-40000-44-444-4000000000000000000000000000000000000000000000000
χ624-4-44-44-44-44-2-22200002-22-2-22000000000000006−6−666−6−6600000000000000000000000000
χ634-4-44-44-44-44-2-22200002-22-2-2200000000000000−666−6−666−600000000000000000000000000
χ644-4-44-4-4444-444-4-40000-4-44-444000000000000000000000000000000000000000000000000
χ654-4-44-4-4444-4-2-222000022-22-2-200000000000000i6−i6−i6i6−i6i6i6−i600000000000000000000000000
χ664-4-44-4-4444-4-2-222000022-22-2-200000000000000−i6i6i6−i6i6−i6−i6i600000000000000000000000000
χ6788-8-80000008-88-80000000000000000000000000000000000000000000000000000000000
χ6888-8-8000000-44-44000000000043−430000000000000000000000000000000000000000000000
χ6988-8-8000000-44-440000000000−43430000000000000000000000000000000000000000000000
χ708-88-80000008-8-880000000000000000000000000000000000000000000000000000000000
χ718-88-8000000-444-4000000000000−4i34i300000000000000000000000000000000000000000000
χ728-88-8000000-444-40000000000004i3−4i300000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).