Finite Group Databasebeta

← Group #10690345

Character table — Group #10690345

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222244444444444444444444888888888888888888888888888888888824242424242424242424242424242424
order12222222222236666666444444446666121212121212121244444444441212121212121212121212121212121212121212121212124444444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ91-11-1-11-1111-1-111-11-1-11-1ii−i−i1-11-111-1-1iiii−i−i−i−i1-1i−ii−i1-1i−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i
χ101-11-1-11-1111-1-111-11-1-11-1ii−i−i1-11-111-1-1iiii−i−i−i−i1-1i−ii−i1-1i−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i-1-111−i−iii-1-111−i−iii
χ111-11-1-11-1111-1-111-11-1-11-1ii−i−i1-11-111-1-1iiii−i−i−i−i-11−iii−i-11−ii-1-111−i−iii11-1-1ii−i−i-1-111−i−iii11-1-1ii−i−i-1-111−i−iii
χ121-11-1-11-1111-1-111-11-1-11-1ii−i−i1-11-111-1-1iiii−i−i−i−i-11−iii−i-11−ii-1-111−i−iii11-1-1ii−i−i-1-111−i−iii-1-111−i−iii11-1-1ii−i−i
χ131-11-1-11-1111-1-111-11-1-11-1−i−iii1-11-111-1-1−i−i−i−iiiii1-1−ii−ii1-1−ii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii
χ141-11-1-11-1111-1-111-11-1-11-1−i−iii1-11-111-1-1−i−i−i−iiiii1-1−ii−ii1-1−ii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii-1-111ii−i−i-1-111ii−i−i
χ151-11-1-11-1111-1-111-11-1-11-1−i−iii1-11-111-1-1−i−i−i−iiiii-11i−i−ii-11i−i-1-111ii−i−i11-1-1−i−iii-1-111ii−i−i11-1-1−i−iii-1-111ii−i−i
χ161-11-1-11-1111-1-111-11-1-11-1−i−iii1-11-111-1-1−i−i−i−iiiii-11i−i−ii-11i−i-1-111ii−i−i11-1-1−i−iii-1-111ii−i−i-1-111ii−i−i11-1-1−i−iii
χ17222222222222222222222222-2-2-2-22222222222220000-2-2000000000000-2-2-2-2-2-2-2-2000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2000022000000000000-2-2-2-22222000000000000000000000000
χ19222222222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ20222222222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2-2-211111111-1-1-1-1-1-1-1-1111111110000000000000000
χ21222222222222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-10000-2-20000−i3i3−i3i3−i3i3−i3i311111111−i3i3−i3i3−i3i3−i3i30000000000000000
χ22222222222222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-10000-2-20000i3−i3i3−i3i3−i3i3−i311111111i3−i3i3−i3i3−i3i3−i30000000000000000
χ23222222222222-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-11111111122-2-2-2-222-2-2-1-1-1-11111-1-1-1-11111-1-1-1-111110000000000000000
χ24222222222222-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-111111111-2-222-2-2-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-10000000000000000
χ25222222222222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111110000220000−i3i3−i3i3i3−i3i3−i31111-1-1-1-1−i3i3−i3i3i3−i3i3−i30000000000000000
χ26222222222222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111110000220000i3−i3i3−i3−i3i3−i3i31111-1-1-1-1i3−i3i3−i3−i3i3−i3i30000000000000000
χ2722222222-2-2-2-22222222200002-2-22-2-2-2-20000000000220000-2-2000022222-22-200000000-2-2-2-20000000000000000
χ2822222222-2-2-2-22222222200002-2-22-2-2-2-20000000000-2-20000220000-2-2-2-22-22-20000000022220000000000000000
χ2922222222-2-2-2-2222222220000-222-2-2-2-2-200000000220000-2-20022220000-22-220000-2-2-2-200000000000000000000
χ3022222222-2-2-2-2222222220000-222-2-2-2-2-200000000-2-200002200-2-2-2-20000-22-220000222200000000000000000000
χ3122222222-2-2-2-2-1-1-1-1-1-1-1-100002-2-221111−i3−i3i3i3−i3−i3i3i300220000-2-2−i3i3−i3i3-1-1-1-1-11-11−i3i3−i3i3i3−i3i3−i311110000000000000000
χ3222222222-2-2-2-2-1-1-1-1-1-1-1-100002-2-221111−i3−i3i3i3−i3−i3i3i300-2-2000022i3−i3i3−i31111-11-11−i3i3−i3i3−i3i3−i3i3-1-1-1-10000000000000000
χ3322222222-2-2-2-2-1-1-1-1-1-1-1-100002-2-221111i3i3−i3−i3i3i3−i3−i300220000-2-2i3−i3i3−i3-1-1-1-1-11-11i3−i3i3−i3−i3i3−i3i311110000000000000000
χ3422222222-2-2-2-2-1-1-1-1-1-1-1-100002-2-221111i3i3−i3−i3i3i3−i3−i300-2-2000022−i3i3−i3i31111-11-11i3−i3i3−i3i3−i3i3−i3-1-1-1-10000000000000000
χ3522222222-2-2-2-2-1-1-1-1-1-1-1-10000-222-21111−i3−i3i3i3−i3−i3i3i3220000-2-200-1-1-1-1−i3i3−i3i31-11-1i3−i3i3−i31111i3−i3i3−i30000000000000000
χ3622222222-2-2-2-2-1-1-1-1-1-1-1-10000-222-21111−i3−i3i3i3−i3−i3i3i3-2-2000022001111i3−i3i3−i31-11-1i3−i3i3−i3-1-1-1-1−i3i3−i3i30000000000000000
χ3722222222-2-2-2-2-1-1-1-1-1-1-1-10000-222-21111i3i3−i3−i3i3i3−i3−i3220000-2-200-1-1-1-1i3−i3i3−i31-11-1−i3i3−i3i31111−i3i3−i3i30000000000000000
χ3822222222-2-2-2-2-1-1-1-1-1-1-1-10000-222-21111i3i3−i3−i3i3i3−i3−i3-2-2000022001111−i3i3−i3i31-11-1−i3i3−i3i3-1-1-1-1i3−i3i3−i30000000000000000
χ3922-22-2-2-222-2-22222-22-2-2-22-22-200002-22-22-22-22-22-2000000000000000000000000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ4022-22-2-2-222-2-22222-22-2-2-22-22-200002-22-22-22-22-22-2000000000000000000000000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ4122-22-2-2-222-2-22222-22-2-2-2-22-2200002-22-2-22-22-22-22000000000000000000000000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ4222-22-2-2-222-2-22222-22-2-2-2-22-2200002-22-2-22-22-22-22000000000000000000000000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ432-22-2-22-2222-2-222-22-2-22-22i2i−2i−2i-22-2222-2-22i2i2i2i−2i−2i−2i−2i0000−2i2i000000000000-2-222−2i−2i2i2i000000000000000000000000
χ442-22-2-22-2222-2-222-22-2-22-2−2i−2i2i2i-22-2222-2-2−2i−2i−2i−2i2i2i2i2i00002i−2i000000000000-2-2222i2i−2i−2i000000000000000000000000
χ452-22-2-22-2222-2-2-1-11-111-112i2i−2i−2i2-22-2-1-111−i−i−i−iiiii2-22i−2i2i−2i2-22i−2i-1-111−i−iii-1-111−i−iii-1-111−i−iii0000000000000000
χ462-22-2-22-2222-2-2-1-11-111-112i2i−2i−2i2-22-2-1-111−i−i−i−iiiii-22−2i2i2i−2i-22−2i2i11-1-1ii−i−i-1-111−i−iii11-1-1ii−i−i0000000000000000
χ472-22-2-22-2222-2-2-1-11-111-112i2i−2i−2i-22-22-1-111−i−i−i−iiiii0000−2i2i0000−i3i3i3−i33−3−3311-1-1ii−i−i−i3i3i3−i33−3−330000000000000000
χ482-22-2-22-2222-2-2-1-11-111-112i2i−2i−2i-22-22-1-111−i−i−i−iiiii0000−2i2i0000i3−i3−i3i3−333−311-1-1ii−i−ii3−i3−i3i3−333−30000000000000000
χ492-22-2-22-2222-2-2-1-11-111-11−2i−2i2i2i2-22-2-1-111iiii−i−i−i−i2-2−2i2i−2i2i2-2−2i2i-1-111ii−i−i-1-111ii−i−i-1-111ii−i−i0000000000000000
χ502-22-2-22-2222-2-2-1-11-111-11−2i−2i2i2i2-22-2-1-111iiii−i−i−i−i-222i−2i−2i2i-222i−2i11-1-1−i−iii-1-111ii−i−i11-1-1−i−iii0000000000000000
χ512-22-2-22-2222-2-2-1-11-111-11−2i−2i2i2i-22-22-1-111iiii−i−i−i−i00002i−2i0000−i3i3i3−i3−333−311-1-1−i−iii−i3i3i3−i3−333−30000000000000000
χ522-22-2-22-2222-2-2-1-11-111-11−2i−2i2i2i-22-22-1-111iiii−i−i−i−i00002i−2i0000i3−i3−i3i33−3−3311-1-1−i−iiii3−i3−i3i33−3−330000000000000000
χ532-22-2-22-22-2-22222-22-2-22-2000022-2-2-2-22200000000002i−2i0000−2i2i00002i2i−2i−2i2-2-2200000000−2i−2i2i2i0000000000000000
χ542-22-2-22-22-2-22222-22-2-22-2000022-2-2-2-2220000000000−2i2i00002i−2i0000−2i−2i2i2i2-2-22000000002i2i−2i−2i0000000000000000
χ552-22-2-22-22-2-22222-22-2-22-20000-2-222-2-222000000002-20000-220022-2-20000-222-20000-2-22200000000000000000000
χ562-22-2-22-22-2-22222-22-2-22-20000-2-222-2-22200000000-2200002-200-2-2220000-222-2000022-2-200000000000000000000
χ572-22-2-22-22-2-222-1-11-111-11000022-2-211-1-133−3−3−3−333002i−2i0000−2i2i−i3i3i3−i3−i−iii-111-13−3−33i3−i3−i3i3ii−i−i0000000000000000
χ582-22-2-22-22-2-222-1-11-111-11000022-2-211-1-133−3−3−3−33300−2i2i00002i−2ii3−i3−i3i3ii−i−i-111-13−3−33−i3i3i3−i3−i−iii0000000000000000
χ592-22-2-22-22-2-222-1-11-111-11000022-2-211-1-1−3−33333−3−3002i−2i0000−2i2ii3−i3−i3i3−i−iii-111-1−333−3−i3i3i3−i3ii−i−i0000000000000000
χ602-22-2-22-22-2-222-1-11-111-11000022-2-211-1-1−3−33333−3−300−2i2i00002i−2i−i3i3i3−i3ii−i−i-111-1−333−3i3−i3−i3i3−i−iii0000000000000000
χ612-22-2-22-22-2-222-1-11-111-110000-2-22211-1-133−3−3−3−3332-20000-2200-1-1113−3−331-1-11−333−311-1-1−333−30000000000000000
χ622-22-2-22-22-2-222-1-11-111-110000-2-22211-1-133−3−3−3−333-2200002-20011-1-1−333−31-1-11−333−3-1-1113−3−330000000000000000
χ632-22-2-22-22-2-222-1-11-111-110000-2-22211-1-1−3−33333−3−32-20000-2200-1-111−333−31-1-113−3−3311-1-13−3−330000000000000000
χ642-22-2-22-22-2-222-1-11-111-110000-2-22211-1-1−3−33333−3−3-2200002-20011-1-13−3−331-1-113−3−33-1-111−333−30000000000000000
χ652-2-2-22-2222-22-222-2-2-22-222i−2i−2i2i00002-2-222i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000000000−i2i2i2−i22−2−22
χ662-2-2-22-2222-22-222-2-2-22-222i−2i−2i2i00002-2-222i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000000000i2−i2−i2i2−222−2
χ672-2-2-22-2222-22-222-2-2-22-22−2i2i2i−2i00002-2-22−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000000000−i2i2i2−i2−222−2
χ682-2-2-22-2222-22-222-2-2-22-22−2i2i2i−2i00002-2-22−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000000000i2−i2−i2i22−2−22
χ69444-44-4-4-400004-444-44-4-400000000000000000000000000000000000000000000000000000000002-22-200000000
χ70444-44-4-4-400004-444-44-4-40000000000000000000000000000000000000000000000000000000000-22-2200000000
χ7144-44-4-4-444-4-44-2-2-22-22224-44-40000-22-22-22-22-22-2200000000000000000000000000000000000000000000000000
χ7244-44-4-4-444-4-44-2-2-22-2222-44-440000-22-222-22-22-22-200000000000000000000000000000000000000000000000000
χ7344-44-4-4-44-444-4444-44-4-4-400000000-44-440000000000000000000000000000000000000000000000000000000000
χ7444-44-4-4-44-444-4-2-2-22-2222000000002-22-2−2i32i32i3−2i3−2i32i32i3−2i300000000000000000000000000000000000000000000000000
χ7544-44-4-4-44-444-4-2-2-22-2222000000002-22-22i3−2i3−2i32i32i3−2i3−2i32i300000000000000000000000000000000000000000000000000
χ7644-4-4-444-400004-44-4-4-4440000000000000000000000000000000000000000000000000000002i−2i2i−2i000000000000
χ7744-4-4-444-400004-44-4-4-444000000000000000000000000000000000000000000000000000000−2i2i−2i2i000000000000
χ784-444-4-44-400004-4-444-4-4400000000000000000000000000000000000000000000000000000000002i−2i−2i2i00000000
χ794-444-4-44-400004-4-444-4-440000000000000000000000000000000000000000000000000000000000−2i2i2i−2i00000000
χ804-4-4444-4-400004-4-4-4444-40000000000000000000000000000000000000000000000000000002i−2i−2i2i000000000000
χ814-4-4444-4-400004-4-4-4444-4000000000000000000000000000000000000000000000000000000−2i2i2i−2i000000000000
χ824-4-4-44-4444-44-4-2-2222-22-24i−4i−4i4i0000-222-2−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000000000000000000000
χ834-4-4-44-4444-44-4-2-2222-22-2−4i4i4i−4i0000-222-22i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000000000000000000000
χ844-4-4-44-444-44-4444-4-4-44-4400000000-444-40000000000000000000000000000000000000000000000000000000000
χ854-4-4-44-444-44-44-2-2222-22-2000000002-2-2223−23−2323−232323−2300000000000000000000000000000000000000000000000000
χ864-4-4-44-444-44-44-2-2222-22-2000000002-2-22−232323−2323−23−232300000000000000000000000000000000000000000000000000
χ87888-88-8-8-80000-44-4-44-4440000000000000000000000000000000000000000000000000000000000000000000000
χ8888-8-8-888-80000-44-4444-4-40000000000000000000000000000000000000000000000000000000000000000000000
χ898-888-8-88-80000-444-4-444-40000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-8888-8-80000-4444-4-4-440000000000000000000000000000000000000000000000000000000000000000000000

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