Finite Group Databasebeta

← Group #10858708

Character table — Group #10858708

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222444444444444444444444444444488888888888888888888888888888881212242424242424242424484848
order1222223444466622444444666666881212121212121212242424244444448881212121212121212121212121212121224242424242488444444888488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-111111111-1-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111-1-1-1
χ41111111111111111111111111111-1-111111111-1-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111
χ51111111111111111-1-111-1-111111111111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1111-1-11-11-1
χ61111111111111111-1-111-1-111111111111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1-1-111-11-11
χ71111111111111111-1-111-1-1111111-1-111111111-1-1-1-11-1-1111-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1111-1-11-1-1-1-111-11
χ81111111111111111-1-111-1-1111111-1-111111111-1-1-1-11-1-1111-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-111-11111-1-11-1
χ911111111111111-1-111-1-11111-1-1-1-111111-1-1-1-1111111-1-11-1-11-1-1111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-111111-1-11
χ1011111111111111-1-111-1-11111-1-1-1-111111-1-1-1-1111111-1-11-1-11-1-1111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-111-1
χ1111111111111111-1-111-1-11111-1-1-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-111-11111-1-111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-111111-1
χ1211111111111111-1-111-1-11111-1-1-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-111-11111-1-111-1-1-1-1-1-11111-1-11111-1-1111111-1-1-1-1-11
χ1311111111111111-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-1-111111-111-1111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-111-111-111-1-111-1-1
χ1411111111111111-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-1-111111-111-1111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-11-1-11-1-111-1-111
χ1511111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111-1-1-1-11-1-1-1-11111-1-1-111-1-111-1-1111111-1-1-1-1-1-1111111-111-1-1-1-1-11-111
χ1611111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111-1-1-1-11-1-1-1-11111-1-1-111-1-111-1-1111111-1-1-1-1-1-11111-1-11-1-111111-11-1-1
χ17222222-12222-1-1-122222222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ18222222-12222-1-1-122222222-1-1-1-1-1-1-2-2-1-1-1-1-1-1-1-11111-222-2-2-2-2-2-2-1-111-1-1-1-1-1-111111111111100000000000000
χ19222222-12222-1-1-122-2-222-2-2-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-22221111111111111111-1-1-1-1-1-100000000000000
χ20222222-12222-1-1-122-2-222-2-2-1-1-1-1-1-1-2-2-1-1-1-1-1-1-1-111112-2-2222-2-2-211-1-1111111-1-1-1-1-1-111111100000000000000
χ21222222-12222-1-1-1-2-222-2-222-1-1111122-1-1-11111-1-1-1-1-12-2-22-2-22-2-2-1-1-1-1-1-11111-1-11111-1-1111100000000000000
χ22222222-12222-1-1-1-2-222-2-222-1-11111-2-2-1-1-11111-11111-2-2-2-222-222-1-111-1-1111111-1-1-1-111-1-1-1-100000000000000
χ23222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1111122-1-1-11111-1-1-1-1-1-222-2222-2-2111111-1-1-1-111-1-1-1-1-1-1111100000000000000
χ24222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-11111-2-2-1-1-11111-111112222-2-2-22211-1-111-1-1-1-1-1-1111111-1-1-1-100000000000000
χ252222-2-222-22-2222002200-2-2-2-20000222-2-2000022222200-200-2002222-2-20000-2-20000-2-2000000000000000000
χ262222-2-222-22-2222002200-2-2-2-20000-2-22-2-200002-2-2-2-2-20020020022-2-2-2-2000022000022000000000000000000
χ272222-2-222-22-222200-2-20022-2-20000222-2-2000022222-200200-200-2-2-2-2220000220000-2-2000000000000000000
χ282222-2-222-22-222200-2-20022-2-20000-2-22-2-200002-2-2-2-2200-200200-2-222220000-2-2000022000000000000000000
χ292222-2-22-22-222222200-2-200-2-2222200-222-2-2-2-2-20000000000000000000000000000000000022200-20000-2000
χ302222-2-22-22-222222200-2-200-2-2222200-222-2-2-2-2-200000000000000000000000000000000000-2-2-200200002000
χ312222-2-22-22-22222-2-2002200-2-2-2-2-2-200-2222222-20000000000000000000000000000000000022-20020000-2000
χ322222-2-22-22-22222-2-2002200-2-2-2-2-2-200-2222222-200000000000000000000000000000000000-2-2200-200002000
χ332222-2-2-12-22-2-1-1-1002200-2-211−i3−i3i3i322-111−i3−i3i3i3-1-1-1-1-1200-200-200-1-1-1-111−i3−i3i3i311−i3−i3i3i311−i3−i3i3i300000000000000
χ342222-2-2-12-22-2-1-1-1002200-2-211−i3−i3i3i3-2-2-111−i3−i3i3i3-11111-200200200-1-11111−i3−i3i3i3-1-1i3i3−i3−i3-1-1i3i3−i3−i300000000000000
χ352222-2-2-12-22-2-1-1-1002200-2-211i3i3−i3−i322-111i3i3−i3−i3-1-1-1-1-1200-200-200-1-1-1-111i3i3−i3−i311i3i3−i3−i311i3i3−i3−i300000000000000
χ362222-2-2-12-22-2-1-1-1002200-2-211i3i3−i3−i3-2-2-111i3i3−i3−i3-11111-200200200-1-11111i3i3−i3−i3-1-1−i3−i3i3i3-1-1−i3−i3i3i300000000000000
χ372222-2-2-12-22-2-1-1-100-2-2002211−i3−i3i3i322-111−i3−i3i3i3-1-1-1-1-1-200200-2001111-1-1i3i3−i3−i3-1-1i3i3−i3−i311−i3−i3i3i300000000000000
χ382222-2-2-12-22-2-1-1-100-2-2002211−i3−i3i3i3-2-2-111−i3−i3i3i3-11111200-20020011-1-1-1-1i3i3−i3−i311−i3−i3i3i3-1-1i3i3−i3−i300000000000000
χ392222-2-2-12-22-2-1-1-100-2-2002211i3i3−i3−i322-111i3i3−i3−i3-1-1-1-1-1-200200-2001111-1-1−i3−i3i3i3-1-1−i3−i3i3i311i3i3−i3−i300000000000000
χ402222-2-2-12-22-2-1-1-100-2-2002211i3i3−i3−i3-2-2-111i3i3−i3−i3-11111200-20020011-1-1-1-1−i3−i3i3i311i3i3−i3−i3-1-1−i3−i3i3i300000000000000
χ412-22-22-2222-2-22-2-22-2002-2002-22-22-20022-22-22-2-2000000000000000000000000000000000000002-20002-20000
χ422-22-22-2222-2-22-2-22-2002-2002-22-22-20022-22-22-2-200000000000000000000000000000000000000-22000-220000
χ432-22-22-2222-2-22-2-2-2200-22002-2-22-220022-2-22-22-2000000000000000000000000000000000000002-2000-220000
χ442-22-22-2222-2-22-2-2-2200-22002-2-22-220022-2-22-22-200000000000000000000000000000000000000-220002-20000
χ452-22-22-22-2-2222-2-2002i−2i002i−2i2-2000000-2-2200002000000002i−2i02-22i−2i002i−2i0000002i−2i2i−2i002-22-200000000000000
χ462-22-22-22-2-2222-2-2002i−2i002i−2i2-2000000-2-220000200000000−2i2i0-222i−2i002i−2i000000−2i2i−2i2i00-22-2200000000000000
χ472-22-22-22-2-2222-2-200−2i2i00−2i2i2-2000000-2-2200002000000002i−2i0-22−2i2i00−2i2i0000002i−2i2i−2i00-22-2200000000000000
χ482-22-22-22-2-2222-2-200−2i2i00−2i2i2-2000000-2-220000200000000−2i2i02-2−2i2i00−2i2i000000−2i2i−2i2i002-22-200000000000000
χ492-22-22-2-1-2-222-111002i−2i002i−2i-11−i3i3i3−i30011-1i3−i3−i3i3-1−i3−i3i3i300002i−2i02-2−ii3−3−ii3−33−33−3−ii−ii−i3i3-11-1100000000000000
χ502-22-22-2-1-2-222-111002i−2i002i−2i-11−i3i3i3−i30011-1i3−i3−i3i3-1i3i3−i3−i30000−2i2i0-22−ii−33−ii3−33−3−33i−ii−ii3−i31-11-100000000000000
χ512-22-22-2-1-2-222-111002i−2i002i−2i-11i3−i3−i3i30011-1−i3i3i3−i3-1−i3−i3i3i30000−2i2i0-22−ii3−3−ii−33−333−3i−ii−i−i3i31-11-100000000000000
χ522-22-22-2-1-2-222-111002i−2i002i−2i-11i3−i3−i3i30011-1−i3i3i3−i3-1i3i3−i3−i300002i−2i02-2−ii−33−ii−33−33−33−ii−iii3−i3-11-1100000000000000
χ532-22-22-2-1-2-222-11100−2i2i00−2i2i-11−i3i3i3−i30011-1i3−i3−i3i3-1−i3−i3i3i30000−2i2i02-2i−i−33i−i−33−33−33i−ii−i−i3i3-11-1100000000000000
χ542-22-22-2-1-2-222-11100−2i2i00−2i2i-11−i3i3i3−i30011-1i3−i3−i3i3-1i3i3−i3−i300002i−2i0-22i−i3−3i−i−33−333−3−ii−iii3−i31-11-100000000000000
χ552-22-22-2-1-2-222-11100−2i2i00−2i2i-11i3−i3−i3i30011-1−i3i3i3−i3-1−i3−i3i3i300002i−2i0-22i−i−33i−i3−33−3−33−ii−ii−i3i31-11-100000000000000
χ562-22-22-2-1-2-222-11100−2i2i00−2i2i-11i3−i3−i3i30011-1−i3i3i3−i3-1i3i3−i3−i30000−2i2i02-2i−i3−3i−i3−33−33−3i−ii−ii3−i3-11-1100000000000000
χ572-22-2-222-222-22-2-22-22i−2i-22−2i2i-222-22-200-22-2-22-222000002i−2i0000002i−2i00−2i2i2i−2i−2i2i00000000000000000000000000
χ582-22-2-222-222-22-2-22-2−2i2i-222i−2i-222-22-200-22-2-22-22200000−2i2i000000−2i2i002i−2i−2i2i2i−2i00000000000000000000000000
χ592-22-2-222-222-22-2-2-222i−2i2-2−2i2i-22-22-2200-22-22-22-2200000−2i2i0000002i−2i00−2i2i−2i2i2i−2i00000000000000000000000000
χ602-22-2-222-222-22-2-2-22−2i2i2-22i−2i-22-22-2200-22-22-22-22000002i−2i000000−2i2i002i−2i2i−2i−2i2i00000000000000000000000000
χ612-22-2-22-1-222-2-1112-22i−2i-22−2i2i1-1-11-11001-111-11-1-1−i3−i3i3i302i−2i000000−ii3−3i−i−iii−i−333−3−33i3−i3−i3i3i3−i300000000000000
χ622-22-2-22-1-222-2-1112-22i−2i-22−2i2i1-1-11-11001-111-11-1-1i3i3−i3−i302i−2i000000−ii−33i−i−iii−i3−3−333−3−i3i3i3−i3−i3i300000000000000
χ632-22-2-22-1-222-2-1112-2−2i2i-222i−2i1-1-11-11001-111-11-1-1−i3−i3i3i30−2i2i000000i−i−33−iii−i−ii3−3−333−3i3−i3−i3i3i3−i300000000000000
χ642-22-2-22-1-222-2-1112-2−2i2i-222i−2i1-1-11-11001-111-11-1-1i3i3−i3−i30−2i2i000000i−i3−3−iii−i−ii−333−3−33−i3i3i3−i3−i3i300000000000000
χ652-22-2-22-1-222-2-111-222i−2i2-2−2i2i1-11-11-1001-11-11-11-1−i3−i3i3i30−2i2i000000−ii3−3i−ii−i−ii−33−333−3i3−i3i3−i3−i3i300000000000000
χ662-22-2-22-1-222-2-111-222i−2i2-2−2i2i1-11-11-1001-11-11-11-1i3i3−i3−i30−2i2i000000−ii−33i−ii−i−ii3−33−3−33−i3i3−i3i3i3−i300000000000000
χ672-22-2-22-1-222-2-111-22−2i2i2-22i−2i1-11-11-1001-11-11-11-1−i3−i3i3i302i−2i000000i−i−33−ii−iii−i3−33−3−33i3−i3i3−i3−i3i300000000000000
χ682-22-2-22-1-222-2-111-22−2i2i2-22i−2i1-11-11-1001-11-11-11-1i3i3−i3−i302i−2i000000i−i3−3−ii−iii−i−33−333−3−i3i3−i3i3i3−i300000000000000
χ694444444-4-4-4-44440000000044000000-4-4-40000-40000000000000000000000000000000000000000000000000
χ70444444-2-4-4-4-4-2-2-200000000-2-2−2i3−2i32i32i3002222i32i3−2i3−2i320000000000000000000000000000000000000000000000000
χ71444444-2-4-4-4-4-2-2-200000000-2-22i32i3−2i3−2i300222−2i3−2i32i32i320000000000000000000000000000000000000000000000000
χ724444-4-4-2-44-44-2-2-24400-4-40022-2-2-2-2002-2-2222220000000000000000000000000000000000000000000000000
χ734444-4-4-2-44-44-2-2-2-4-4004400222222002-2-2-2-2-2-220000000000000000000000000000000000000000000000000
χ7444-4-40040000-44-40000000000000022−220000000022−2222−22000000000000000000000000000000022−2200002-2000000
χ7544-4-40040000-44-40000000000000022−220000000022−2222−220000000000000000000000000000000−22220000-22000000
χ7644-4-40040000-44-400000000000000−222200000000−2222−2222000000000000000000000000000000022−220000-22000000
χ7744-4-40040000-44-400000000000000−222200000000−2222−22220000000000000000000000000000000−222200002-2000000
χ784-44-44-4-244-4-4-2224-4004-400-22-22-2200-2-22-22-2220000000000000000000000000000000000000000000000000
χ794-44-44-4-244-4-4-222-4400-4400-222-22-200-2-222-22-220000000000000000000000000000000000000000000000000
χ804-44-4-4444-4-444-4-400000000-440000004-440000-40000000000000000000000000000000000000000000000000
χ814-44-4-44-24-4-44-222000000002-2−2i32i32i3−2i300-22-2−2i32i32i3−2i320000000000000000000000000000000000000000000000000
χ824-44-4-44-24-4-44-222000000002-22i3−2i3−2i32i300-22-22i3−2i3−2i32i320000000000000000000000000000000000000000000000000
χ8388-8-800-400004-440000000000000042−4200000000−2222−2222000000000000000000000000000000000000000000000
χ8488-8-800-400004-4400000000000000−42420000000022−2222−22000000000000000000000000000000000000000000000
χ858-8-880080000-8-880000000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-8800-4000044-40000000000000000000000002i6−2i6−2i62i6000000000000000000000000000000000000000000000
χ878-8-8800-4000044-4000000000000000000000000−2i62i62i6−2i6000000000000000000000000000000000000000000000

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