Finite Group Databasebeta

← Group #10840224

Character table — Group #10840224

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222444444444444444444444444444444444444888888888888888888888888882424242424242424242424244848
order122222223444466666662244444444446666121212121212121212121212121212121212121224444444661212121212121212121212121212121222448888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111
χ411111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111111111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-11-1
χ61111111111111111111111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-111-11
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111-1-1111-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-111-1-1-11
χ911111111111111111111-1-111-1-1111111-1-1-1-111111111-1-1-1-111111111-111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ1011111111111111111111-1-111-1-1111111-1-1-1-111111111-1-1-1-111111111-111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ1111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-111-1-1-1-11111-1-111111111-1-1-1-11111-1-1
χ1211111111111111111111-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-111
χ1311111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111111111111-1-111-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-111-11
χ1411111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111111111111-1-111-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-11-1
χ1511111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-1-11111-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-11
χ1611111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-1-11111-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1111-1
χ17222222222-2-2-2-222222222222220000-2-222222222-2-2-2-2222200000000-20000-200-2-2-2-200000000-2-2000000000000000000
χ18222222222-2-2-2-2222222222-2-2-2-20000222222-2-2-2-2-2-2-2-2-2-2-2-20000000020000-200222200000000-2-2000000000000000000
χ19222222222-2-2-2-22222222-2-222-2-20000-2-2-2-2-2-22222-2-2-2-2-2-2-2-2000000002000020022-2-20000000022000000000000000000
χ20222222222-2-2-2-22222222-2-2-2-222000022-2-2-2-2-2-2-2-2-2-2-2-2222200000000-20000200-2-2220000000022000000000000000000
χ2122222222-12222-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111112-2-2-2-22-2-2-1-1-1-111111111-1-1111100000000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-22222-2-2-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-2-2-2-2-2222111111111111-1-1-1-1-1-100000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-2-2-1-1-1-11111-1-1-1-1111111111111-222222-2-21111-1-1-1-1-1-1-1-1-1-1111100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-222-2-22222221111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-222-2-2-2-2-211-1-1-1-1-1-1111111111100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-222-2-2-2-2-2-2221111-1-1-1-1-1-1-1-1111111111111-2-2-222-22211-1-11111-1-1-1-111-1-1-1-100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2222222-2-211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-2-222-2-2-2-1-1111111-1-1-1-111111100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-2-211111111-1-1-1-1-1-1-1-111111111222-2-2-222-1-111-1-1-1-1111111-1-1-1-100000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-12222220000-2-2-1-1-1-1-1-1-1-11111-1-1-1-1−i3−i3−i3−i3i3i3i3i3-20000-2001111−i3−i3i3i3−i3−i3i3i311−i3−i3i3i300000000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-12222220000-2-2-1-1-1-1-1-1-1-11111-1-1-1-1i3i3i3i3−i3−i3−i3−i3-20000-2001111i3i3−i3−i3i3i3−i3−i311i3i3−i3−i300000000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-2000022-1-1-1-1111111111111−i3−i3−i3−i3i3i3i3i320000-200-1-1-1-1i3i3−i3−i3i3i3−i3−i311−i3−i3i3i300000000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-2000022-1-1-1-1111111111111i3i3i3i3−i3−i3−i3−i320000-200-1-1-1-1−i3−i3i3i3−i3−i3i3i311i3i3−i3−i300000000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-20000-2-21111-1-1-1-111111111−i3−i3−i3−i3i3i3i3i320000200-1-111−i3−i3i3i3i3i3−i3−i3-1-1i3i3−i3−i300000000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-20000-2-21111-1-1-1-111111111i3i3i3i3−i3−i3−i3−i320000200-1-111i3i3−i3−i3−i3−i3i3i3-1-1−i3−i3i3i300000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-222000022111111111111-1-1-1-1−i3−i3−i3−i3i3i3i3i3-2000020011-1-1i3i3−i3−i3−i3−i3i3i3-1-1i3i3−i3−i300000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-222000022111111111111-1-1-1-1i3i3i3i3−i3−i3−i3−i3-2000020011-1-1−i3−i3i3i3i3i3−i3−i3-1-1−i3−i3i3i300000000000000
χ3722-2-22-22-222-2-22-222-2-22-2002-2002i2i−2i−2i2-2000022-2-222-2-200002i2i−2i−2i2i2i−2i−2i02i−2i00000002-22i−2i2i−2i000000000000000000000000
χ3822-2-22-22-222-2-22-222-2-22-2002-200−2i−2i2i2i2-2000022-2-222-2-20000−2i−2i2i2i−2i−2i2i2i0−2i2i00000002-2−2i2i−2i2i000000000000000000000000
χ3922-2-22-22-222-2-22-222-2-22-200-22002i2i−2i−2i-220000-2-22222-2-200002i2i−2i−2i2i2i−2i−2i0−2i2i0000000-22−2i2i−2i2i000000000000000000000000
χ4022-2-22-22-222-2-22-222-2-22-200-2200−2i−2i2i2i-220000-2-22222-2-20000−2i−2i2i2i−2i−2i2i2i02i−2i0000000-222i−2i2i−2i000000000000000000000000
χ4122-2-22-22-22-222-2-222-2-22-2002-2000000-22000022-2-2-2-2220000000000000002i−2i02i−2i00-2200002i−2i2i−2i002i−2i2i−2i00000000000000
χ4222-2-22-22-22-222-2-222-2-22-2002-2000000-22000022-2-2-2-222000000000000000−2i2i0−2i2i00-220000−2i2i−2i2i00−2i2i−2i2i00000000000000
χ4322-2-22-22-22-222-2-222-2-22-200-220000002-20000-2-222-2-2220000000000000002i−2i0−2i2i002-200002i−2i2i−2i00−2i2i−2i2i00000000000000
χ4422-2-22-22-22-222-2-222-2-22-200-220000002-20000-2-222-2-222000000000000000−2i2i02i−2i002-20000−2i2i−2i2i002i−2i2i−2i00000000000000
χ4522-2-22-22-2-12-2-221-1-111-11002-2002i2i−2i−2i2-2−i3−i3i3i3-1-111-1-111−i3−i3i3i3−i−iii−i−iii02i−2i00000−i3i3-11−ii−ii3−3−33−i3i33−3−3300000000000000
χ4622-2-22-22-2-12-2-221-1-111-11002-2002i2i−2i−2i2-2i3i3−i3−i3-1-111-1-111i3i3−i3−i3−i−iii−i−iii02i−2i00000i3−i3-11−ii−ii−333−3i3−i3−333−300000000000000
χ4722-2-22-22-2-12-2-221-1-111-11002-200−2i−2i2i2i2-2−i3−i3i3i3-1-111-1-111−i3−i3i3i3ii−i−iii−i−i0−2i2i00000−i3i3-11i−ii−i−333−3−i3i3−333−300000000000000
χ4822-2-22-22-2-12-2-221-1-111-11002-200−2i−2i2i2i2-2i3i3−i3−i3-1-111-1-111i3i3−i3−i3ii−i−iii−i−i0−2i2i00000i3−i3-11i−ii−i3−3−33i3−i33−3−3300000000000000
χ4922-2-22-22-2-12-2-221-1-111-1100-22002i2i−2i−2i-22−i3−i3i3i311-1-1-1-111i3i3−i3−i3−i−iii−i−iii0−2i2i00000i3−i31-1i−ii−i−333−3−i3i33−3−3300000000000000
χ5022-2-22-22-2-12-2-221-1-111-1100-22002i2i−2i−2i-22i3i3−i3−i311-1-1-1-111−i3−i3i3i3−i−iii−i−iii0−2i2i00000−i3i31-1i−ii−i3−3−33i3−i3−333−300000000000000
χ5122-2-22-22-2-12-2-221-1-111-1100-2200−2i−2i2i2i-22−i3−i3i3i311-1-1-1-111i3i3−i3−i3ii−i−iii−i−i02i−2i00000i3−i31-1−ii−ii3−3−33−i3i3−333−300000000000000
χ5222-2-22-22-2-12-2-221-1-111-1100-2200−2i−2i2i2i-22i3i3−i3−i311-1-1-1-111−i3−i3i3i3ii−i−iii−i−i02i−2i00000−i3i31-1−ii−ii−333−3i3−i33−3−3300000000000000
χ5322-2-22-22-2-1-222-21-1-111-11002-2000000-22−i3−i3i3i3-1-11111-1-1−i3−i3i3i333−3−3−3−3330002i−2i02i−2ii3−i31-13−3−33−ii−iii3−i3−ii−ii00000000000000
χ5422-2-22-22-2-1-222-21-1-111-11002-2000000-22−i3−i3i3i3-1-11111-1-1−i3−i3i3i3−3−33333−3−3000−2i2i0−2i2ii3−i31-1−333−3i−ii−ii3−i3i−ii−i00000000000000
χ5522-2-22-22-2-1-222-21-1-111-11002-2000000-22i3i3−i3−i3-1-11111-1-1i3i3−i3−i333−3−3−3−333000−2i2i0−2i2i−i3i31-13−3−33i−ii−i−i3i3i−ii−i00000000000000
χ5622-2-22-22-2-1-222-21-1-111-11002-2000000-22i3i3−i3−i3-1-11111-1-1i3i3−i3−i3−3−33333−3−30002i−2i02i−2i−i3i31-1−333−3−ii−ii−i3i3−ii−ii00000000000000
χ5722-2-22-22-2-1-222-21-1-111-1100-220000002-2−i3−i3i3i311-1-111-1-1i3i3−i3−i333−3−3−3−333000−2i2i02i−2i−i3i3-11−333−3i−ii−ii3−i3−ii−ii00000000000000
χ5822-2-22-22-2-1-222-21-1-111-1100-220000002-2−i3−i3i3i311-1-111-1-1i3i3−i3−i3−3−33333−3−30002i−2i0−2i2i−i3i3-113−3−33−ii−iii3−i3i−ii−i00000000000000
χ5922-2-22-22-2-1-222-21-1-111-1100-220000002-2i3i3−i3−i311-1-111-1-1−i3−i3i3i333−3−3−3−3330002i−2i0−2i2ii3−i3-11−333−3−ii−ii−i3i3i−ii−i00000000000000
χ6022-2-22-22-2-1-222-21-1-111-1100-220000002-2i3i3−i3−i311-1-111-1-1−i3−i3i3i3−3−33333−3−3000−2i2i02i−2ii3−i3-113−3−33i−ii−i−i3i3−ii−ii00000000000000
χ612-22-222-2-2222-2-2-2-2-22-2220000002-22-200000000002-22-200002-22-22-22-200000000000000000000000000002i−2i002i−2i000000
χ622-22-222-2-2222-2-2-2-2-22-2220000002-22-200000000002-22-200002-22-22-22-20000000000000000000000000000−2i2i00−2i2i000000
χ632-22-222-2-2222-2-2-2-2-22-222000000-22-2200000000002-22-20000-22-22-22-2200000000000000000000000000002i−2i00−2i2i000000
χ642-22-222-2-2222-2-2-2-2-22-222000000-22-2200000000002-22-20000-22-22-22-220000000000000000000000000000−2i2i002i−2i000000
χ652-2-222-2-2222-22-22-2-2-222-20000002i−2i−2i2i00000000002-2-2200002i−2i−2i2i2i−2i−2i2i000000000000000000000000002-2002i−2i00000000
χ662-2-222-2-2222-22-22-2-2-222-20000002i−2i−2i2i00000000002-2-2200002i−2i−2i2i2i−2i−2i2i00000000000000000000000000-2200−2i2i00000000
χ672-2-222-2-2222-22-22-2-2-222-2000000−2i2i2i−2i00000000002-2-220000−2i2i2i−2i−2i2i2i−2i000000000000000000000000002-200−2i2i00000000
χ682-2-222-2-2222-22-22-2-2-222-2000000−2i2i2i−2i00000000002-2-220000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000-22002i−2i00000000
χ69444-4-4-4-444000044-44-4-4-40000000000000000000000000000000000000000000000000000000000000000000000−2i22i20000
χ70444-4-4-4-444000044-44-4-4-400000000000000000000000000000000000000000000000000000000000000000000002i2−2i20000
χ7144-44-44-4-440000-44-4-44-44000000000000000000000000000000000000000000000000000000000000000000000000−2i22i200
χ7244-44-44-4-440000-44-4-44-440000000000000000000000000000000000000000000000000000000000000000000000002i2−2i200
χ734-444-4-44-440000-4-4444-4-400004i−4i0000000000000000004i−4i4i−4i000000000000000000000000000000000000000000000000
χ744-444-4-44-440000-4-4444-4-40000−4i4i000000000000000000−4i4i−4i4i000000000000000000000000000000000000000000000000
χ754-444-4-44-4-2000022-2-2-22200004i−4i000000−2i32i3−2i32i323−2323−230000−2i2i−2i2i000000000000000000000000000000000000000000000000
χ764-444-4-44-4-2000022-2-2-22200004i−4i0000002i3−2i32i3−2i3−2323−23230000−2i2i−2i2i000000000000000000000000000000000000000000000000
χ774-444-4-44-4-2000022-2-2-2220000−4i4i000000−2i32i3−2i32i3−2323−232300002i−2i2i−2i000000000000000000000000000000000000000000000000
χ784-444-4-44-4-2000022-2-2-2220000−4i4i0000002i3−2i32i3−2i323−2323−2300002i−2i2i−2i000000000000000000000000000000000000000000000000
χ794-44-444-4-44-4-444-4-4-44-44400000000000000000000-44-440000000000000000000000000000000000000000000000000000
χ804-44-444-4-4-244-4-4222-22-2-20000004-44-40000000000-22-220000-22-22-22-220000000000000000000000000000000000000000
χ814-44-444-4-4-244-4-4222-22-2-2000000-44-440000000000-22-2200002-22-22-22-20000000000000000000000000000000000000000
χ824-44-444-4-4-2-4-444222-22-2-2000000000000000000002-22-20000−2i32i3−2i32i32i3−2i32i3−2i30000000000000000000000000000000000000000
χ834-44-444-4-4-2-4-444222-22-2-2000000000000000000002-22-200002i3−2i32i3−2i3−2i32i3−2i32i30000000000000000000000000000000000000000
χ844-4-444-4-444-44-444-4-4-444-400000000000000000000-444-40000000000000000000000000000000000000000000000000000
χ854-4-444-4-44-24-44-4-2222-2-220000004i−4i−4i4i0000000000-222-20000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000000000000000
χ864-4-444-4-44-24-44-4-2222-2-22000000−4i4i4i−4i0000000000-222-200002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000000000000000
χ874-4-444-4-44-2-44-44-2222-2-22000000000000000000002-2-22000023−23−2323−232323−230000000000000000000000000000000000000000
χ884-4-444-4-44-2-44-44-2222-2-22000000000000000000002-2-220000−232323−2323−23−23230000000000000000000000000000000000000000
χ894-4-4-4-4444400004-44-4-4-444-400000000004-4-44000000000000000000000000000000000000000000000000000000000000
χ904-4-4-4-4444400004-44-4-4-44-440000000000-444-4000000000000000000000000000000000000000000000000000000000000
χ914-4-4-4-4444-20000-22-2222-24-40000000000-222-223−23−2323000023−23−2323000000000000000000000000000000000000000000000000
χ924-4-4-4-4444-20000-22-2222-24-40000000000-222-2−232323−230000−232323−23000000000000000000000000000000000000000000000000
χ934-4-4-4-4444-20000-22-2222-2-4400000000002-2-2223−23−23230000−232323−23000000000000000000000000000000000000000000000000
χ944-4-4-4-4444-20000-22-2222-2-4400000000002-2-22−232323−23000023−23−2323000000000000000000000000000000000000000000000000
χ95888-8-8-8-88-40000-4-44-44440000000000000000000000000000000000000000000000000000000000000000000000000000
χ9688-88-88-8-8-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000000000000000

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