Finite Group Databasebeta

← Group #10840286

Character table — Group #10840286

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222444444444444444444448888888888888888888888888888888888242424242424242448484848
order124422234446661212121244446688881212242424242424242424446688888812121212121212121212242424242424242424242424224444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-111-1-11-11-1
χ6111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-111-11-11
χ7111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-11111-1-1-1-11111-1-1-1-11-11-111-1-1-11-11
χ8111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-11111-1-1-1-11111-1-1-1-1-11-11-1-1111-11-1
χ9111111111111111111-1-1-1-1111111111111111111-1-111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111
χ10111111111111111111-1-1-1-1111111111111111111-1-111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ11111111111111111111-1-1-1-11111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ12111111111111111111-1-1-1-11111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ13111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111-11-1-1-111-111-1
χ14111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1111-1-11-1-11
χ15111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111111111111-11-1-1-1111-1-11
χ16111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111111111-11-1111-1-1-111-1
χ172222222-1222-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ182222222-1222-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-211-2-2-2-222111111-1-1-1-111111111-1-1-1-1000000000000
χ192222222-1222-1-1-1-1-1-1-12222-1-1-2-2-2-2-1-11111111122-2-2-1-122-2-2-2-21111-1-1-1-1-1-1-1-1-1-111111111000000000000
χ202222222-1222-1-1-1-1-1-1-12222-1-1-2-2-2-2-1-111111111-2-22211-2-222-2-2-1-1-1-111-1-1-1-11111-1-1-1-11111000000000000
χ212222222-1222-1-1-1-1-1-1-1-2-2-2-2-1-12222-1-1-1-1-1-1-1-1-1-122-2-2-1-1-2-222-2-21111-1-111111111-1-1-1-11111000000000000
χ222222222-1222-1-1-1-1-1-1-1-2-2-2-2-1-12222-1-1-1-1-1-1-1-1-1-1-2-2221122-2-2-2-2-1-1-1-1111111-1-1-1-111111111000000000000
χ232222222-1222-1-1-1-1-1-1-1-2-2-2-2-1-1-2-2-2-2-1-1111111112222-1-1-2-2-2-222-1-1-1-1-1-1111111111111-1-1-1-1000000000000
χ242222222-1222-1-1-1-1-1-1-1-2-2-2-2-1-1-2-2-2-2-1-111111111-2-2-2-2112222221111111111-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ2522222-2-22-22-222222220000-2-222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000002i−2i2i−2i0000
χ2622222-2-22-22-222222220000-2-222-2-2-2-22222-2-2-2-200000000000000000000000000000000000000−2i2i−2i2i0000
χ2722222-2-22-22-222222220000-2-2-2-222-2-2-2-2-2-22222000000000000000000000000000000000000002i−2i−2i2i0000
χ2822222-2-22-22-222222220000-2-2-2-222-2-2-2-2-2-2222200000000000000000000000000000000000000−2i2i2i−2i0000
χ292222-2-2222-2-2-2-2222-2-222-2-2-2200002-200000000002i−2i00002i−2i002i2i−2i−2i0022-2-200002i2i−2i−2i0000000000000000
χ302222-2-2222-2-2-2-2222-2-222-2-2-2200002-20000000000−2i2i0000−2i2i00−2i−2i2i2i0022-2-20000−2i−2i2i2i0000000000000000
χ312222-2-2222-2-2-2-2222-2-2-2-222-2200002-200000000002i−2i0000−2i2i002i2i−2i−2i00-2-2220000−2i−2i2i2i0000000000000000
χ322222-2-2222-2-2-2-2222-2-2-2-222-2200002-20000000000−2i2i00002i−2i00−2i−2i2i2i00-2-22200002i2i−2i−2i0000000000000000
χ332222-2-22-12-2-211-1-1-11122-2-21-10000-1133−3−333−3−3002i−2i−i3i3002i−2i00−i−iii−i3i3-1-111−i3−i3i3i3−i−iii33−3−3000000000000
χ342222-2-22-12-2-211-1-1-11122-2-21-10000-1133−3−333−3−300−2i2ii3−i300−2i2i00ii−i−ii3−i3-1-111i3i3−i3−i3ii−i−i33−3−3000000000000
χ352222-2-22-12-2-211-1-1-11122-2-21-10000-11−3−333−3−333002i−2ii3−i3002i−2i00−i−iiii3−i3-1-111i3i3−i3−i3−i−iii−3−333000000000000
χ362222-2-22-12-2-211-1-1-11122-2-21-10000-11−3−333−3−33300−2i2i−i3i300−2i2i00ii−i−i−i3i3-1-111−i3−i3i3i3ii−i−i−3−333000000000000
χ372222-2-22-12-2-211-1-1-111-2-2221-10000-1133−3−333−3−3002i−2ii3−i300−2i2i00−i−iiii3−i311-1-1−i3−i3i3i3ii−i−i−3−333000000000000
χ382222-2-22-12-2-211-1-1-111-2-2221-10000-1133−3−333−3−300−2i2i−i3i3002i−2i00ii−i−i−i3i311-1-1i3i3−i3−i3−i−iii−3−333000000000000
χ392222-2-22-12-2-211-1-1-111-2-2221-10000-11−3−333−3−333002i−2i−i3i300−2i2i00−i−iii−i3i311-1-1i3i3−i3−i3ii−i−i33−3−3000000000000
χ402222-2-22-12-2-211-1-1-111-2-2221-10000-11−3−333−3−33300−2i2ii3−i3002i−2i00ii−i−ii3−i311-1-1−i3−i3i3i3−i−iii33−3−3000000000000
χ4122-2-22-2-222-22222-2-2-2-22i−2i2i−2i-2-2000022000000002-200222i−2i00000000-2-22i−2i2i−2i2i−2i2i−2i00000000000000000000
χ4222-2-22-2-222-22222-2-2-2-22i−2i2i−2i-2-200002200000000-2200-2-2−2i2i00000000222i−2i2i−2i−2i2i−2i2i00000000000000000000
χ4322-2-22-2-222-22222-2-2-2-2−2i2i−2i2i-2-2000022000000002-20022−2i2i00000000-2-2−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ4422-2-22-2-222-22222-2-2-2-2−2i2i−2i2i-2-200002200000000-2200-2-22i−2i0000000022−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ4522-2-22-2-2-12-22-1-1-111112i−2i2i−2i110000-1-13−33−33−33−32-200-1-12i−2i0000−i3i3−i3i311−ii−ii−ii−ii3−33−3−i3i3−i3i3000000000000
χ4622-2-22-2-2-12-22-1-1-111112i−2i2i−2i110000-1-13−33−33−33−3-220011−2i2i0000i3−i3i3−i3-1-1−ii−iii−ii−i−33−33−i3i3−i3i3000000000000
χ4722-2-22-2-2-12-22-1-1-111112i−2i2i−2i110000-1-1−33−33−33−332-200-1-12i−2i0000i3−i3i3−i311−ii−ii−ii−ii−33−33i3−i3i3−i3000000000000
χ4822-2-22-2-2-12-22-1-1-111112i−2i2i−2i110000-1-1−33−33−33−33-220011−2i2i0000−i3i3−i3i3-1-1−ii−iii−ii−i3−33−3i3−i3i3−i3000000000000
χ4922-2-22-2-2-12-22-1-1-11111−2i2i−2i2i110000-1-13−33−33−33−32-200-1-1−2i2i0000i3−i3i3−i311i−ii−ii−ii−i3−33−3i3−i3i3−i3000000000000
χ5022-2-22-2-2-12-22-1-1-11111−2i2i−2i2i110000-1-13−33−33−33−3-2200112i−2i0000−i3i3−i3i3-1-1i−ii−i−ii−ii−33−33i3−i3i3−i3000000000000
χ5122-2-22-2-2-12-22-1-1-11111−2i2i−2i2i110000-1-1−33−33−33−332-200-1-1−2i2i0000−i3i3−i3i311i−ii−ii−ii−i−33−33−i3i3−i3i3000000000000
χ5222-2-22-2-2-12-22-1-1-11111−2i2i−2i2i110000-1-1−33−33−33−33-2200112i−2i0000i3−i3i3−i3-1-1i−ii−i−ii−ii3−33−3−i3i3−i3i3000000000000
χ5322-2-2-22-2222-2-2-22-2-2222i−2i−2i2i2-22-22-22-22-2-222-2-2200000000002i−2i0000002i−2i−2i2i00000000−2i2i2i−2i000000000000
χ5422-2-2-22-2222-2-2-22-2-2222i−2i−2i2i2-2-22-222-2-222-2-222-20000000000−2i2i0000002i−2i−2i2i000000002i−2i−2i2i000000000000
χ5522-2-2-22-2222-2-2-22-2-222−2i2i2i−2i2-22-22-22-22-2-222-2-220000000000−2i2i000000−2i2i2i−2i000000002i−2i−2i2i000000000000
χ5622-2-2-22-2222-2-2-22-2-222−2i2i2i−2i2-2-22-222-2-222-2-222-200000000002i−2i000000−2i2i2i−2i00000000−2i2i2i−2i000000000000
χ5722-2-2-22-2-122-211-111-1-12i−2i−2i2i-112-22-2-11-111-1-111-10000−i3i300002i−2i−333−3i3−i3−iii−i3−3−33−i3i3i3−i3i−i−ii000000000000
χ5822-2-2-22-2-122-211-111-1-12i−2i−2i2i-112-22-2-11-111-1-111-10000i3−i300002i−2i3−3−33−i3i3−iii−i−333−3i3−i3−i3i3i−i−ii000000000000
χ5922-2-2-22-2-122-211-111-1-12i−2i−2i2i-11-22-22-111-1-111-1-110000−i3i30000−2i2i3−3−33i3−i3−iii−i3−3−33i3−i3−i3i3−iii−i000000000000
χ6022-2-2-22-2-122-211-111-1-12i−2i−2i2i-11-22-22-111-1-111-1-110000i3−i30000−2i2i−333−3−i3i3−iii−i−333−3−i3i3i3−i3−iii−i000000000000
χ6122-2-2-22-2-122-211-111-1-1−2i2i2i−2i-112-22-2-11-111-1-111-10000−i3i30000−2i2i3−3−33i3−i3i−i−ii−333−3−i3i3i3−i3−iii−i000000000000
χ6222-2-2-22-2-122-211-111-1-1−2i2i2i−2i-112-22-2-11-111-1-111-10000i3−i30000−2i2i−333−3−i3i3i−i−ii3−3−33i3−i3−i3i3−iii−i000000000000
χ6322-2-2-22-2-122-211-111-1-1−2i2i2i−2i-11-22-22-111-1-111-1-110000−i3i300002i−2i−333−3i3−i3i−i−ii−333−3i3−i3−i3i3i−i−ii000000000000
χ6422-2-2-22-2-122-211-111-1-1−2i2i2i−2i-11-22-22-111-1-111-1-110000i3−i300002i−2i3−3−33−i3i3i−i−ii3−3−33−i3i3i3−i3i−i−ii000000000000
χ6522-2-2-2-222-222-2-22-2-2220000-222-2-22-222-2-22-222-2000000000000000000000000000000000022-2-200000000
χ6622-2-2-2-222-222-2-22-2-2220000-222-2-22-222-2-22-222-20000000000000000000000000000000000-2-22200000000
χ6722-2-2-2-222-222-2-22-2-2220000-22-222-2-22-222-22-2-2200000000000000000000000000000000002-2-2200000000
χ6822-2-2-2-222-222-2-22-2-2220000-22-222-2-22-222-22-2-220000000000000000000000000000000000-222-200000000
χ6944444-4-4-2-44-4-2-2-2-2-2-2-200002244-4-422-2-2-2-222220000000000000000000000000000000000000000000000
χ7044444-4-4-2-44-4-2-2-2-2-2-2-2000022-4-444222222-2-2-2-20000000000000000000000000000000000000000000000
χ714444-44-44-4-44-4-4444-4-400004-40000-44000000000000000000000000000000000000000000000000000000
χ724444-44-4-2-4-4422-2-2-2220000-2200002-22323−23−23−23−2323230000000000000000000000000000000000000000000000
χ734444-44-4-2-4-4422-2-2-2220000-2200002-2−23−2323232323−23−230000000000000000000000000000000000000000000000
χ7444-4-44444-4-4-4444-4-4-4-40000440000-4-4000000000000000000000000000000000000000000000000000000
χ7544-4-4444-2-4-4-4-2-2-222220000-2-200002223−2323−23−2323−23230000000000000000000000000000000000000000000000
χ7644-4-4444-2-4-4-4-2-2-222220000-2-2000022−2323−232323−2323−230000000000000000000000000000000000000000000000
χ7744-4-4-4-44-2-44422-222-2-200002-24-4-442-2-222-22-2-220000000000000000000000000000000000000000000000
χ7844-4-4-4-44-2-44422-222-2-200002-2-444-42-22-2-22-222-20000000000000000000000000000000000000000000000
χ798-88i−8i000800000-88i−8i00000000000000000000000000000000000000000000000000000000000000000000
χ808-88i−8i000-4000−4i34i34−4i4i43−43000000000000000000000000000000000000000000000000000000000000000000
χ818-88i−8i000-40004i3−4i34−4i4i−4343000000000000000000000000000000000000000000000000000000000000000000
χ828-8−8i8i000800000-8−8i8i00000000000000000000000000000000000000000000000000000000000000000000
χ838-8−8i8i000-4000−4i34i344i−4i−4343000000000000000000000000000000000000000000000000000000000000000000
χ848-8−8i8i000-40004i3−4i344i−4i43−43000000000000000000000000000000000000000000000000000000000000000000

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