Finite Group Databasebeta

← Group #10859092

Character table — Group #10859092

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222444444444444444444444444444444444444888888888888888888888888882424242424242424242424244848
order12222222344446666666224444444444666612121212121212121212121212121212121212124444444412121212121212121212121212121212121244448888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111
χ411111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111111111-1-1111111-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-11111-1-1-1-1
χ61111111111111111111111-1-1111111-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111
χ71111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-111-1-1
χ81111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ911111111111111111111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1111111111111-1-111-11-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-11-1
χ1011111111111111111111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1111111111111-1-111-11-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111-11
χ1111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111111-1
χ1211111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1111-1-11111-1-1-1-1-1-1111111-1-1111111-1-1-1-1-11
χ1311111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111111111-1-11-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-11
χ1411111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111111111-1-11-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111-11111-1-1-1-1-1-11111-1-1111111-1-111-1-111-1-1-11
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111-11111-1-1-1-1-1-11111-1-11111-1-111-1-111-1-1111-1
χ17222222222-2-2-2-222222222222-2-2000022222222222222-2-2-2-2000000000000-2-200-2-20000-2-20000-2-2000000000000000000
χ18222222222-2-2-2-2222222222-2-2-2-20000-2-22222-2-2-2-2-2-2-2-2-2-2-2-20000000000002200220000-2-2000022000000000000000000
χ19222222222-2-2-2-22222222-2-222220000-2-2-2-2-2-22222-2-2-2-2-2-2-2-20000000000002-200220000220000-2-2000000000000000000
χ20222222222-2-2-2-22222222-2-2-2-222000022-2-2-2-2-2-2-2-22222-2-2-2-2000000000000-2200-2-2000022000022000000000000000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-2-2-2-222-2-2-1-11111-1-11111-1-1111100000000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2222222-2-2-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222111111-1-1111111-1-1-1-100000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-222-2-2-2-2-2-2-1-1-1-111111111-1-1-1-1111111112222-2-2-2-211-1-1-1-1-1-1-1-1-1-111111100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-222-2-22222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-2-222-22-2-211111111-1-1-1-1-1-1111100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-222-2-2-2-2-2-2-2-21111-1-1-1-11111-1-1-1-11111111122-2-2-222211-1-1-1-1111111-1-1-1-1-1-100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-222222211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-22-2-2-2-1-1-1-1-1-111111111111100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-22211111111-1-1-1-1-1-1-1-111111111-2-2222-222-1-1111111-1-1-1-111-1-1-1-100000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2000022-1-1-1-1-1-1-1-1-1-1-1-11111−i3−i3−i3−i3i3i3i3i30000-2-20011−i3−i3i3i311−i3−i3i3i311−i3−i3i3i300000000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2000022-1-1-1-1-1-1-1-1-1-1-1-11111i3i3i3i3−i3−i3−i3−i30000-2-20011i3i3−i3−i311i3i3−i3−i311i3i3−i3−i300000000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-20000-2-2-1-1-1-1111111111111−i3−i3−i3−i3i3i3i3i300002200-1-1i3i3−i3−i311i3i3−i3−i3-1-1−i3−i3i3i300000000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-20000-2-2-1-1-1-1111111111111i3i3i3i3−i3−i3−i3−i300002200-1-1−i3−i3i3i311−i3−i3i3i3-1-1i3i3−i3−i300000000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222220000-2-21111-1-1-1-111111111−i3−i3−i3−i3i3i3i3i300002-200-1-1i3i3−i3−i3-1-1−i3−i3i3i311i3i3−i3−i300000000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222220000-2-21111-1-1-1-111111111i3i3i3i3−i3−i3−i3−i300002-200-1-1−i3−i3i3i3-1-1i3i3−i3−i311−i3−i3i3i300000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-22200002211111111-1-1-1-11111−i3−i3−i3−i3i3i3i3i30000-220011−i3−i3i3i3-1-1i3i3−i3−i3-1-1i3i3−i3−i300000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-22200002211111111-1-1-1-11111i3i3i3i3−i3−i3−i3−i30000-220011i3i3−i3−i3-1-1−i3−i3i3i3-1-1−i3−i3i3i300000000000000
χ3722-222-2-2-2222-2-22-2-2-222-22-2002-200000022-2-20000000022-2-2000000002-22-20000002-22-22-22-22-200000000000000000000
χ3822-222-2-2-2222-2-22-2-2-222-22-2002-200000022-2-20000000022-2-200000000-22-22000000-22-222-2-22-2200000000000000000000
χ3922-222-2-2-2222-2-22-2-2-222-2-2200-22000000-2-2220000000022-2-2000000002-2-220000002-22-2-22-22-2200000000000000000000
χ4022-222-2-2-2222-2-22-2-2-222-2-2200-22000000-2-2220000000022-2-200000000-222-2000000-22-22-222-22-200000000000000000000
χ4122-222-2-2-22-2-2222-2-2-222-22-200-222i2i−2i−2i0022-2-200000000-2-2222i2i−2i−2i2i2i−2i−2i0000002i−2i000000-220000002i−2i2i−2i00000000000000
χ4222-222-2-2-22-2-2222-2-2-222-22-200-22−2i−2i2i2i0022-2-200000000-2-222−2i−2i2i2i−2i−2i2i2i000000−2i2i000000-22000000−2i2i−2i2i00000000000000
χ4322-222-2-2-22-2-2222-2-2-222-2-22002-22i2i−2i−2i00-2-22200000000-2-2222i2i−2i−2i2i2i−2i−2i000000−2i2i0000002-2000000−2i2i−2i2i00000000000000
χ4422-222-2-2-22-2-2222-2-2-222-2-22002-2−2i−2i2i2i00-2-22200000000-2-222−2i−2i2i2i−2i−2i2i2i0000002i−2i0000002-20000002i−2i2i−2i00000000000000
χ4522-222-2-2-2-122-2-2-1111-1-112-2002-2000000-1-11133−3−333−3−3-1-11133−3−3−3−3332-22-200003−3-11-11-11-11-113−33−3−3300000000000000
χ4622-222-2-2-2-122-2-2-1111-1-112-2002-2000000-1-11133−3−333−3−3-1-111−3−33333−3−3-22-2200003−31-11-1-111-11-13−3−333−300000000000000
χ4722-222-2-2-2-122-2-2-1111-1-112-2002-2000000-1-111−3−333−3−333-1-11133−3−3−3−333-22-220000−331-11-1-111-11-1−333−3−3300000000000000
χ4822-222-2-2-2-122-2-2-1111-1-112-2002-2000000-1-111−3−333−3−333-1-111−3−33333−3−32-22-20000−33-11-11-11-11-11−33−333−300000000000000
χ4922-222-2-2-2-122-2-2-1111-1-11-2200-2200000011-1-133−3−3−3−333-1-11133−3−3−3−333-222-20000−331-11-11-1-11-113−3−333−300000000000000
χ5022-222-2-2-2-122-2-2-1111-1-11-2200-2200000011-1-133−3−3−3−333-1-111−3−33333−3−32-2-220000−33-11-111-11-11-13−33−3−3300000000000000
χ5122-222-2-2-2-122-2-2-1111-1-11-2200-2200000011-1-1−3−33333−3−3-1-11133−3−3−3−3332-2-2200003−3-11-111-11-11-1−33−333−300000000000000
χ5222-222-2-2-2-122-2-2-1111-1-11-2200-2200000011-1-1−3−33333−3−3-1-111−3−33333−3−3-222-200003−31-11-11-1-11-11−333−3−3300000000000000
χ5322-222-2-2-2-1-2-222-1111-1-112-200-222i2i−2i−2i00-1-11133−3−333−3−311-1-1−i−iii−i−iii0000002i−2i−33−i3i3i3−i31-1−i3i3i3−i3−33−ii−ii00000000000000
χ5422-222-2-2-2-1-2-222-1111-1-112-200-222i2i−2i−2i00-1-111−3−333−3−33311-1-1−i−iii−i−iii0000002i−2i3−3i3−i3−i3i31-1i3−i3−i3i33−3−ii−ii00000000000000
χ5522-222-2-2-2-1-2-222-1111-1-112-200-22−2i−2i2i2i00-1-11133−3−333−3−311-1-1ii−i−iii−i−i000000−2i2i−33i3−i3−i3i31-1i3−i3−i3i3−33i−ii−i00000000000000
χ5622-222-2-2-2-1-2-222-1111-1-112-200-22−2i−2i2i2i00-1-111−3−333−3−33311-1-1ii−i−iii−i−i000000−2i2i3−3−i3i3i3−i31-1−i3i3i3−i33−3i−ii−i00000000000000
χ5722-222-2-2-2-1-2-222-1111-1-11-22002-22i2i−2i−2i0011-1-133−3−3−3−33311-1-1−i−iii−i−iii000000−2i2i3−3i3−i3−i3i3-11−i3i3i3−i3−33i−ii−i00000000000000
χ5822-222-2-2-2-1-2-222-1111-1-11-22002-22i2i−2i−2i0011-1-1−3−33333−3−311-1-1−i−iii−i−iii000000−2i2i−33−i3i3i3−i3-11i3−i3−i3i33−3i−ii−i00000000000000
χ5922-222-2-2-2-1-2-222-1111-1-11-22002-2−2i−2i2i2i0011-1-133−3−3−3−33311-1-1ii−i−iii−i−i0000002i−2i3−3−i3i3i3−i3-11i3−i3−i3i3−33−ii−ii00000000000000
χ6022-222-2-2-2-1-2-222-1111-1-11-22002-2−2i−2i2i2i0011-1-1−3−33333−3−311-1-1ii−i−iii−i−i0000002i−2i−33i3−i3−i3i3-11−i3i3i3−i33−3−ii−ii00000000000000
χ612-22-22-22-222-22-2-22-2-2-2220000002-22-2000000000000002-22-22-22-22-22-200000000000000000000000000002i−2i00002i−2i0000
χ622-22-22-22-222-22-2-22-2-2-2220000002-22-2000000000000002-22-22-22-22-22-20000000000000000000000000000−2i2i0000−2i2i0000
χ632-22-22-22-222-22-2-22-2-2-222000000-22-22000000000000002-22-2-22-22-22-2200000000000000000000000000002i−2i0000−2i2i0000
χ642-22-22-22-222-22-2-22-2-2-222000000-22-22000000000000002-22-2-22-22-22-220000000000000000000000000000−2i2i00002i−2i0000
χ652-2-2-222-222-222-2-2-222-22-20000002i−2i−2i2i00000000000000-222-22i−2i−2i2i2i−2i−2i2i000000000000000000000000002-200002i−2i000000
χ662-2-2-222-222-222-2-2-222-22-20000002i−2i−2i2i00000000000000-222-22i−2i−2i2i2i−2i−2i2i00000000000000000000000000-220000−2i2i000000
χ672-2-2-222-222-222-2-2-222-22-2000000−2i2i2i−2i00000000000000-222-2−2i2i2i−2i−2i2i2i−2i000000000000000000000000002-20000−2i2i000000
χ682-2-2-222-222-222-2-2-222-22-2000000−2i2i2i−2i00000000000000-222-2−2i2i2i−2i−2i2i2i−2i00000000000000000000000000-2200002i−2i000000
χ69444-4-4-4-4440000444-4-4-4-4004-40000000000004-44-400000000000000000000000000000000000000000000000000000000
χ70444-4-4-4-4440000444-4-4-4-400-44000000000000-44-4400000000000000000000000000000000000000000000000000000000
χ71444-4-4-4-44-20000-2-2-22222004-400000000−2i32i3−2i32i3-22-22−2i32i3−2i32i30000000000000000000000000000000000000000000000000000
χ72444-4-4-4-44-20000-2-2-22222004-4000000002i3−2i32i3−2i3-22-222i3−2i32i3−2i30000000000000000000000000000000000000000000000000000
χ73444-4-4-4-44-20000-2-2-2222200-4400000000−2i32i3−2i32i32-22-22i3−2i32i3−2i30000000000000000000000000000000000000000000000000000
χ74444-4-4-4-44-20000-2-2-2222200-44000000002i3−2i32i3−2i32-22-2−2i32i3−2i32i30000000000000000000000000000000000000000000000000000
χ7544-4-4-444-4400004-4-44-4-4400000000004i−4i000000004i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ7644-4-4-444-4400004-4-44-4-440000000000−4i4i00000000−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ7744-4-4-444-4-20000-222-222-200000000004i−4i−2i32i32i3−2i323−23−2323−2i2i2i−2i0000000000000000000000000000000000000000000000000000
χ7844-4-4-444-4-20000-222-222-200000000004i−4i2i3−2i3−2i32i3−232323−23−2i2i2i−2i0000000000000000000000000000000000000000000000000000
χ7944-4-4-444-4-20000-222-222-20000000000−4i4i−2i32i32i3−2i3−232323−232i−2i−2i2i0000000000000000000000000000000000000000000000000000
χ8044-4-4-444-4-20000-222-222-20000000000−4i4i2i3−2i3−2i32i323−23−23232i−2i−2i2i0000000000000000000000000000000000000000000000000000
χ814-444-44-4-440000-44-444-4-400000000000000000000000000000000000000000000000000000000000000000000000022−2200
χ824-444-44-4-440000-44-444-4-4000000000000000000000000000000000000000000000000000000000000000000000000−222200
χ834-44-44-44-44-44-44-44-4-4-444000000000000000000000000-44-44000000000000000000000000000000000000000000000000
χ844-44-44-44-4-24-44-42-2222-2-20000004-44-400000000000000-22-22-22-22-22-220000000000000000000000000000000000000000
χ854-44-44-44-4-24-44-42-2222-2-2000000-44-4400000000000000-22-222-22-22-22-20000000000000000000000000000000000000000
χ864-44-44-44-4-2-44-442-2222-2-20000000000000000000000002-22-2−2i32i3−2i32i32i3−2i32i3−2i30000000000000000000000000000000000000000
χ874-44-44-44-4-2-44-442-2222-2-20000000000000000000000002-22-22i3−2i32i3−2i3−2i32i3−2i32i30000000000000000000000000000000000000000
χ884-4-44-4-44440000-4-44-44-4400000000000000000000000000000000000000000000000000000000000000000022−2200000000
χ894-4-44-4-44440000-4-44-44-44000000000000000000000000000000000000000000000000000000000000000000−222200000000
χ904-4-4-444-4444-4-44-4-444-44-40000000000000000000000004-4-44000000000000000000000000000000000000000000000000
χ914-4-4-444-44-24-4-4422-2-22-22000000000000000000000000-222-223−23−2323−232323−230000000000000000000000000000000000000000
χ924-4-4-444-44-24-4-4422-2-22-22000000000000000000000000-222-2−232323−2323−23−23230000000000000000000000000000000000000000
χ934-4-4-444-44-2-444-422-2-22-220000004i−4i−4i4i000000000000002-2-22−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000000000000000
χ944-4-4-444-44-2-444-422-2-22-22000000−4i4i4i−4i000000000000002-2-222i−2i−2i2i2i−2i−2i2i0000000000000000000000000000000000000000
χ958-888-88-8-8-400004-44-4-4440000000000000000000000000000000000000000000000000000000000000000000000000000
χ968-8-88-8-888-4000044-44-44-40000000000000000000000000000000000000000000000000000000000000000000000000000

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