Finite Group Databasebeta

← Group #10840280

Character table — Group #10840280

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222444444444444444444448888888888888888888888888888888888242424242424242448484848
order1244222344466612121212444466888812121212121212121212224444446666881212121212121212121212122424242424242424244488884488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-111111111111-11-111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11-11-1
χ6111111111111111111111111-1-1-1-111111111111-11-111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-11-11
χ7111111111111111111111111-1-1-1-11111111111-11-11-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-11-11
χ8111111111111111111111111-1-1-1-11111111111-11-11-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1111-11-1
χ9111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-111-1-111
χ10111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1
χ11111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-111-1-1-1-11111-1-1
χ12111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-11111-1-1-1-111
χ13111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111-11-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1
χ14111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111-11-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-11
χ15111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-11-1111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-11
χ16111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-11-1111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1
χ172222222-1222-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ182222222-1222-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111122111111111111-1-1-1-1-1-1-1-1000000000000
χ192222222-1222-1-1-1-1-1-1-12222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-12-22-222-2-2-1-111-2-2-1-1-1-1-1-111111111111111000000000000
χ202222222-1222-1-1-1-1-1-1-12222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1-22-22-2-22211-1-1-2-2111111-1-1-1-1-1-111111111000000000000
χ212222222-1222-1-1-1-1-1-1-1-2-2-2-2-1-1222211111111-1-12222-2-2-2-2-1-1-1-1-2-2-1-11111-1-11111-1-1-1-11111000000000000
χ222222222-1222-1-1-1-1-1-1-1-2-2-2-2-1-1222211111111-1-1-2-2-2-222221111-2-211-1-1-1-111-1-1-1-1-1-1-1-11111000000000000
χ232222222-1222-1-1-1-1-1-1-1-2-2-2-2-1-1-2-2-2-211111111-1-12-22-2-2-222-1-11122-1-1111111-1-1-1-11111-1-1-1-1000000000000
χ242222222-1222-1-1-1-1-1-1-1-2-2-2-2-1-1-2-2-2-211111111-1-1-22-2222-2-211-1-12211-1-1-1-1-1-111111111-1-1-1-1000000000000
χ2522222-2-222-2-2222222222-2-2-2-200002222-2-2-2-2-2-20000000000000000000000000000000000002i−2i002i−2i0000
χ2622222-2-222-2-2222222222-2-2-2-200002222-2-2-2-2-2-2000000000000000000000000000000000000−2i2i00−2i2i0000
χ2722222-2-222-2-22222222-2-222-2-20000-2-2-2-22222-2-20000000000000000000000000000000000002i−2i00−2i2i0000
χ2822222-2-222-2-22222222-2-222-2-20000-2-2-2-22222-2-2000000000000000000000000000000000000−2i2i002i−2i0000
χ292222-22-22-22-22-2-222-2-200002-222-2-2000000002-200002i−2i2i−2i000000002i2i−2i−2i002i2i−2i−2i22-2-20000000000000000
χ302222-22-22-22-22-2-222-2-200002-222-2-2000000002-20000−2i2i−2i2i00000000−2i−2i2i2i00−2i−2i2i2i22-2-20000000000000000
χ312222-22-22-22-22-2-222-2-200002-2-2-222000000002-200002i−2i−2i2i000000002i2i−2i−2i00−2i−2i2i2i-2-2220000000000000000
χ322222-22-22-22-22-2-222-2-200002-2-2-222000000002-20000−2i2i2i−2i00000000−2i−2i2i2i002i2i−2i−2i-2-2220000000000000000
χ332222-22-2-1-22-2-111-1-1110000-1122-2-233−3−333−3−3-1100002i−2i2i−2i−i3i3−i3i300−i3i3−i−iii−i3i3−i−iii-1-11133−3−3000000000000
χ342222-22-2-1-22-2-111-1-1110000-1122-2-233−3−333−3−3-110000−2i2i−2i2ii3−i3i3−i300i3−i3ii−i−ii3−i3ii−i−i-1-11133−3−3000000000000
χ352222-22-2-1-22-2-111-1-1110000-1122-2-2−3−333−3−333-1100002i−2i2i−2ii3−i3i3−i300i3−i3−i−iiii3−i3−i−iii-1-111−3−333000000000000
χ362222-22-2-1-22-2-111-1-1110000-1122-2-2−3−333−3−333-110000−2i2i−2i2i−i3i3−i3i300−i3i3ii−i−i−i3i3ii−i−i-1-111−3−333000000000000
χ372222-22-2-1-22-2-111-1-1110000-11-2-22233−3−333−3−3-1100002i−2i−2i2i−i3i3i3−i300−i3i3−i−iiii3−i3ii−i−i11-1-1−3−333000000000000
χ382222-22-2-1-22-2-111-1-1110000-11-2-22233−3−333−3−3-110000−2i2i2i−2ii3−i3−i3i300i3−i3ii−i−i−i3i3−i−iii11-1-1−3−333000000000000
χ392222-22-2-1-22-2-111-1-1110000-11-2-222−3−333−3−333-1100002i−2i−2i2ii3−i3−i3i300i3−i3−i−iii−i3i3ii−i−i11-1-133−3−3000000000000
χ402222-22-2-1-22-2-111-1-1110000-11-2-222−3−333−3−333-110000−2i2i2i−2i−i3i3i3−i300−i3i3ii−i−ii3−i3−i−iii11-1-133−3−3000000000000
χ4122-2-22-2-22-222222-2-2-2-20000-2-22-22-2000000002222-2-20000222200-2-20000-2-200002-22-20000000000000000
χ4222-2-22-2-22-222222-2-2-2-20000-2-22-22-20000000022-2-2220000-2-2-2-2002200002200002-22-20000000000000000
χ4322-2-22-2-22-222222-2-2-2-20000-2-2-22-2200000000222-2-22000022-2-200-2-20000220000-22-220000000000000000
χ4422-2-22-2-22-222222-2-2-2-20000-2-2-22-220000000022-222-20000-2-22200220000-2-20000-22-220000000000000000
χ4522-2-22-2-2-1-222-1-1-111110000112-22-2−i3i3−i3i3−i3i3−i3i3-1-122-2-20000-1-1-1-10011−i3i3−i3i311−i3i3−i3i3-11-11−i3i3−i3i3000000000000
χ4622-2-22-2-2-1-222-1-1-111110000112-22-2−i3i3−i3i3−i3i3−i3i3-1-1-2-2220000111100-1-1i3−i3i3−i3-1-1i3−i3i3−i3-11-11−i3i3−i3i3000000000000
χ4722-2-22-2-2-1-222-1-1-111110000112-22-2i3−i3i3−i3i3−i3i3−i3-1-122-2-20000-1-1-1-10011i3−i3i3−i311i3−i3i3−i3-11-11i3−i3i3−i3000000000000
χ4822-2-22-2-2-1-222-1-1-111110000112-22-2i3−i3i3−i3i3−i3i3−i3-1-1-2-2220000111100-1-1−i3i3−i3i3-1-1−i3i3−i3i3-11-11i3−i3i3−i3000000000000
χ4922-2-22-2-2-1-222-1-1-11111000011-22-22−i3i3−i3i3−i3i3−i3i3-1-12-2-220000-1-1110011−i3i3−i3i3-1-1i3−i3i3−i31-11-1i3−i3i3−i3000000000000
χ5022-2-22-2-2-1-222-1-1-11111000011-22-22−i3i3−i3i3−i3i3−i3i3-1-1-222-2000011-1-100-1-1i3−i3i3−i311−i3i3−i3i31-11-1i3−i3i3−i3000000000000
χ5122-2-22-2-2-1-222-1-1-11111000011-22-22i3−i3i3−i3i3−i3i3−i3-1-12-2-220000-1-1110011i3−i3i3−i3-1-1−i3i3−i3i31-11-1−i3i3−i3i3000000000000
χ5222-2-22-2-2-1-222-1-1-11111000011-22-22i3−i3i3−i3i3−i3i3−i3-1-1-222-2000011-1-100-1-1−i3i3−i3i311i3−i3i3−i31-11-1−i3i3−i3i3000000000000
χ5322-2-2-22-222-222-2-2-2-2222i−2i2i−2i2-200002i−2i−2i2i−2i2i2i−2i-2200000000000000000000000000000000002-2002i−2i000000
χ5422-2-2-22-222-222-2-2-2-2222i−2i2i−2i2-200002i−2i−2i2i−2i2i2i−2i-220000000000000000000000000000000000-2200−2i2i000000
χ5522-2-2-22-222-222-2-2-2-222−2i2i−2i2i2-20000−2i2i2i−2i2i−2i−2i2i-2200000000000000000000000000000000002-200−2i2i000000
χ5622-2-2-22-222-222-2-2-2-222−2i2i−2i2i2-20000−2i2i2i−2i2i−2i−2i2i-220000000000000000000000000000000000-22002i−2i000000
χ5722-2-2-2-22222-22-2-2-2-2222i−2i−2i2i-222-2-222i−2i−2i2i2i−2i−2i2i2-20000000000002i−2i0000000000002-2-222i−2i−2i2i000000000000
χ5822-2-2-2-22222-22-2-2-2-2222i−2i−2i2i-22-222-22i−2i−2i2i2i−2i−2i2i2-2000000000000−2i2i000000000000-222-2−2i2i2i−2i000000000000
χ5922-2-2-2-22222-22-2-2-2-222−2i2i2i−2i-222-2-22−2i2i2i−2i−2i2i2i−2i2-2000000000000−2i2i0000000000002-2-22−2i2i2i−2i000000000000
χ6022-2-2-2-22222-22-2-2-2-222−2i2i2i−2i-22-222-2−2i2i2i−2i−2i2i2i−2i2-20000000000002i−2i000000000000-222-22i−2i−2i2i000000000000
χ6122-2-2-2-22-122-2-11111-1-12i−2i−2i2i1-12-2-22−iii−i−iii−i-1100000000−i3i3−i3i32i−2ii3−i33−3−33i3−i33−3−33-111-1−iii−i000000000000
χ6222-2-2-2-22-122-2-11111-1-12i−2i−2i2i1-12-2-22−iii−i−iii−i-1100000000i3−i3i3−i32i−2i−i3i3−333−3−i3i3−333−3-111-1−iii−i000000000000
χ6322-2-2-2-22-122-2-11111-1-12i−2i−2i2i1-1-222-2−iii−i−iii−i-1100000000−i3i3i3−i3−2i2ii3−i33−3−33−i3i3−333−31-1-11i−i−ii000000000000
χ6422-2-2-2-22-122-2-11111-1-12i−2i−2i2i1-1-222-2−iii−i−iii−i-1100000000i3−i3−i3i3−2i2i−i3i3−333−3i3−i33−3−331-1-11i−i−ii000000000000
χ6522-2-2-2-22-122-2-11111-1-1−2i2i2i−2i1-12-2-22i−i−iii−i−ii-1100000000−i3i3−i3i3−2i2ii3−i3−333−3i3−i3−333−3-111-1i−i−ii000000000000
χ6622-2-2-2-22-122-2-11111-1-1−2i2i2i−2i1-12-2-22i−i−iii−i−ii-1100000000i3−i3i3−i3−2i2i−i3i33−3−33−i3i33−3−33-111-1i−i−ii000000000000
χ6722-2-2-2-22-122-2-11111-1-1−2i2i2i−2i1-1-222-2i−i−iii−i−ii-1100000000−i3i3i3−i32i−2ii3−i3−333−3−i3i33−3−331-1-11−iii−i000000000000
χ6822-2-2-2-22-122-2-11111-1-1−2i2i2i−2i1-1-222-2i−i−iii−i−ii-1100000000i3−i3−i3i32i−2i−i3i33−3−33i3−i3−333−31-1-11−iii−i000000000000
χ6944444-4-4-24-4-4-2-2-2-2-2-2-244-4-4220000-2-2-2-22222220000000000000000000000000000000000000000000000
χ7044444-4-4-24-4-4-2-2-2-2-2-2-2-4-4442200002222-2-2-2-2220000000000000000000000000000000000000000000000
χ714444-4-444-4-444-4-444-4-40000-44000000000000-440000000000000000000000000000000000000000000000
χ724444-4-44-2-4-44-222-2-22200002-200002323−23−23−23−2323232-20000000000000000000000000000000000000000000000
χ734444-4-44-2-4-44-222-2-22200002-20000−23−2323232323−23−232-20000000000000000000000000000000000000000000000
χ7444-4-44444-4-4-4444-4-4-4-4000044000000000000-4-40000000000000000000000000000000000000000000000
χ7544-4-4444-2-4-4-4-2-2-222220000-2-20000−2i32i3−2i32i32i3−2i32i3−2i3220000000000000000000000000000000000000000000000
χ7644-4-4444-2-4-4-4-2-2-222220000-2-200002i3−2i32i3−2i3−2i32i3−2i32i3220000000000000000000000000000000000000000000000
χ7744-4-4-44-4-24-44-22222-2-24i−4i4i−4i-220000−2i2i2i−2i2i−2i−2i2i2-20000000000000000000000000000000000000000000000
χ7844-4-4-44-4-24-44-22222-2-2−4i4i−4i4i-2200002i−2i−2i2i−2i2i2i−2i2-20000000000000000000000000000000000000000000000
χ798-88i−8i0008000-8008i−8i00000000000000000000000000000000000000000000000000000000000000000000
χ808-88i−8i000-40004−4i34i3−4i4i43−43000000000000000000000000000000000000000000000000000000000000000000
χ818-88i−8i000-400044i3−4i3−4i4i−4343000000000000000000000000000000000000000000000000000000000000000000
χ828-8−8i8i0008000-800−8i8i00000000000000000000000000000000000000000000000000000000000000000000
χ838-8−8i8i000-40004−4i34i34i−4i−4343000000000000000000000000000000000000000000000000000000000000000000
χ848-8−8i8i000-400044i3−4i34i−4i43−43000000000000000000000000000000000000000000000000000000000000000000

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