Finite Group Databasebeta

← Group #10859017

Character table — Group #10859017

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222444444444444444444444444444444444444888888888888888888888888882424242424242424242424244848
order122222223444466666662244444444441212121212121212121212121212121212121212121212122244444466666612121212121212121212121244448888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111
χ41111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111111111-1-111-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-111-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1
χ61111111111111111111111-1-111-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-111-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111
χ71111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-1
χ81111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ911111111111111111111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-11-1-1-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-11-1
χ1011111111111111111111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-11-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111-11
χ1111111111111111111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-111111-1
χ1211111111111111111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111-1-1111111-1-1-1-1-1-11111-1-1111111-1-1-1-1-11
χ1311111111111111111111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111111111111111-1-11-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-111-11
χ1411111111111111111111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111111111111111-1-11-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-11-1
χ1511111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1-11
χ1611111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-1111-1
χ17222222222-2-2-2-222222222222-2-2-2-200002222-2-2-2-2-2-2-2-2-2-2-2-2000000000000200-2220000-2-2000022000000000000000000
χ18222222222-2-2-2-2222222222-2-2-2-2220000-2-2-2-2-2-2-2-2-2-2-2-22222000000000000-2002220000220000-2-2000000000000000000
χ19222222222-2-2-2-22222222-2-222222200002222-2-2-2-222222222000000000000-200-2-2-20000-2-20000-2-2000000000000000000
χ20222222222-2-2-2-22222222-2-2-2-222-2-20000-2-2-2-2-2-2-2-22222-2-2-2-20000000000002002-2-2000022000022000000000000000000
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
χ2222222222-12222-1-1-1-1-1-1-122222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-2-2-2-22-2-22-1-11111-1-11111-1-1111100000000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-222-2-222221111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-2-2-2-2-222-2-1-1111111111111-1-1-1-100000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-222-2-2-2-2-2-21111-1-1-1-1-1-1-1-11111111111112222-2-2-2-2-1-1-1-1-1-111-1-1-1-111111100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-222-2-2-2-22222-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-2-222-2-2-22111111-1-1-1-1-1-111111100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111122-2-2-222211-1-1-1-1-1-1111111-1-1-1-100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-22222221111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-122-2-22-2-2-211-1-1-1-1111111-1-1111100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-222-2-2-2-21111-1-1-1-11111-1-1-1-111111111-2-222222-211111111-1-1-1-1-1-1-1-1-1-100000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-20000-1-1-1-1111111111111−i3−i3−i3−i3i3i3i3i30000200-2-1-1−i3−i3i3i311−i3−i3i3i3-1-1−i3−i3i3i300000000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-20000-1-1-1-1111111111111i3i3i3i3−i3−i3−i3−i30000200-2-1-1i3i3−i3−i311i3i3−i3−i3-1-1i3i3−i3−i300000000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-2220000111111111111-1-1-1-1−i3−i3−i3−i3i3i3i3i30000-2002-1-1i3i3−i3−i3-1-1i3i3−i3−i311−i3−i3i3i300000000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-2220000111111111111-1-1-1-1i3i3i3i3−i3−i3−i3−i30000-2002-1-1−i3−i3i3i3-1-1−i3−i3i3i311i3i3−i3−i300000000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222220000-1-1-1-11111-1-1-1-1-1-1-1-1−i3−i3−i3−i3i3i3i3i30000-200-211i3i3−i3−i311−i3−i3i3i311i3i3−i3−i300000000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222220000-1-1-1-11111-1-1-1-1-1-1-1-1i3i3i3i3−i3−i3−i3−i30000-200-211−i3−i3i3i311i3i3−i3−i311−i3−i3i3i300000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-222-2-2000011111111-1-1-1-11111−i3−i3−i3−i3i3i3i3i30000200211−i3−i3i3i3-1-1i3i3−i3−i3-1-1i3i3−i3−i300000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-222-2-2000011111111-1-1-1-11111i3i3i3i3−i3−i3−i3−i30000200211i3i3−i3−i3-1-1−i3−i3i3i3-1-1−i3−i3i3i300000000000000
χ3722-222-2-2-2222-2-22-2-222-2-22-2002-2000000000022-2-222-2-20000000000002-22-200002-22-22-2002-22-200000000000000000000
χ3822-222-2-2-2222-2-22-2-222-2-22-2002-2000000000022-2-222-2-2000000000000-22-2200002-2-22-2200-22-2200000000000000000000
χ3922-222-2-2-2222-2-22-2-222-2-2-2200-22000000000022-2-2-2-2220000000000002-2-220000-222-22-200-22-2200000000000000000000
χ4022-222-2-2-2222-2-22-2-222-2-2-2200-22000000000022-2-2-2-222000000000000-222-20000-22-22-22002-22-200000000000000000000
χ4122-222-2-2-22-2-2222-2-222-2-22-200-22002i2i−2i−2i0000-2-222-2-22200002i2i−2i−2i2i2i−2i−2i000002i−2i02-20000000000002i−2i2i−2i00000000000000
χ4222-222-2-2-22-2-2222-2-222-2-22-200-2200−2i−2i2i2i0000-2-222-2-2220000−2i−2i2i2i−2i−2i2i2i00000−2i2i02-2000000000000−2i2i−2i2i00000000000000
χ4322-222-2-2-22-2-2222-2-222-2-2-22002-2002i2i−2i−2i0000-2-22222-2-200002i2i−2i−2i2i2i−2i−2i00000−2i2i0-22000000000000−2i2i−2i2i00000000000000
χ4422-222-2-2-22-2-2222-2-222-2-2-22002-200−2i−2i2i2i0000-2-22222-2-20000−2i−2i2i2i−2i−2i2i2i000002i−2i0-220000000000002i−2i2i−2i00000000000000
χ4522-222-2-2-2-122-2-2-111-1-1112-2002-200000033−3−3-1-111-1-11133−3−333−3−3−3−3332-22-20000-11-11-113−3-11-113−33−3−3300000000000000
χ4622-222-2-2-2-122-2-2-111-1-1112-2002-200000033−3−3-1-111-1-11133−3−3−3−33333−3−3-22-220000-111-11-13−31-11-13−3−333−300000000000000
χ4722-222-2-2-2-122-2-2-111-1-1112-2002-2000000−3−333-1-111-1-111−3−33333−3−3−3−333-22-220000-111-11-1−331-11-1−333−3−3300000000000000
χ4822-222-2-2-2-122-2-2-111-1-1112-2002-2000000−3−333-1-111-1-111−3−333−3−33333−3−32-22-20000-11-11-11−33-11-11−33−333−300000000000000
χ4922-222-2-2-2-122-2-2-111-1-111-2200-2200000033−3−3-1-11111-1-1−3−33333−3−3−3−333-222-200001-11-11-13−3-11-11−33−333−300000000000000
χ5022-222-2-2-2-122-2-2-111-1-111-2200-2200000033−3−3-1-11111-1-1−3−333−3−33333−3−32-2-2200001-1-11-113−31-11-1−333−3−3300000000000000
χ5122-222-2-2-2-122-2-2-111-1-111-2200-22000000−3−333-1-11111-1-133−3−333−3−3−3−3332-2-2200001-1-11-11−331-11-13−3−333−300000000000000
χ5222-222-2-2-2-122-2-2-111-1-111-2200-22000000−3−333-1-11111-1-133−3−3−3−33333−3−3-222-200001-11-11-1−33-11-113−33−3−3300000000000000
χ5322-222-2-2-2-1-2-222-111-1-1112-200-22002i2i−2i−2i33−3−311-1-111-1-1−3−333−i−iii−i−iii000002i−2i0-11−i3i3i3−i3−33−i3i3i3−i33−3−ii−ii00000000000000
χ5422-222-2-2-2-1-2-222-111-1-1112-200-22002i2i−2i−2i−3−33311-1-111-1-133−3−3−i−iii−i−iii000002i−2i0-11i3−i3−i3i33−3i3−i3−i3i3−33−ii−ii00000000000000
χ5522-222-2-2-2-1-2-222-111-1-1112-200-2200−2i−2i2i2i33−3−311-1-111-1-1−3−333ii−i−iii−i−i00000−2i2i0-11i3−i3−i3i3−33i3−i3−i3i33−3i−ii−i00000000000000
χ5622-222-2-2-2-1-2-222-111-1-1112-200-2200−2i−2i2i2i−3−33311-1-111-1-133−3−3ii−i−iii−i−i00000−2i2i0-11−i3i3i3−i33−3−i3i3i3−i3−33i−ii−i00000000000000
χ5722-222-2-2-2-1-2-222-111-1-111-22002-2002i2i−2i−2i33−3−311-1-1-1-11133−3−3−i−iii−i−iii00000−2i2i01-1i3−i3−i3i3−33−i3i3i3−i3−33i−ii−i00000000000000
χ5822-222-2-2-2-1-2-222-111-1-111-22002-2002i2i−2i−2i−3−33311-1-1-1-111−3−333−i−iii−i−iii00000−2i2i01-1−i3i3i3−i33−3i3−i3−i3i33−3i−ii−i00000000000000
χ5922-222-2-2-2-1-2-222-111-1-111-22002-200−2i−2i2i2i33−3−311-1-1-1-11133−3−3ii−i−iii−i−i000002i−2i01-1−i3i3i3−i3−33i3−i3−i3i3−33−ii−ii00000000000000
χ6022-222-2-2-2-1-2-222-111-1-111-22002-200−2i−2i2i2i−3−33311-1-1-1-111−3−333ii−i−iii−i−i000002i−2i01-1i3−i3−i3i33−3−i3i3i3−i33−3−ii−ii00000000000000
χ612-222-2-2-2222-22-2-2222-2-2-2000000002i−2i2i−2i00002-22-2000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000002-200002i−2i0000
χ622-222-2-2-2222-22-2-2222-2-2-2000000002i−2i2i−2i00002-22-2000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000-220000−2i2i0000
χ632-222-2-2-2222-22-2-2222-2-2-200000000−2i2i−2i2i00002-22-200000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000002-20000−2i2i0000
χ642-222-2-2-2222-22-2-2222-2-2-200000000−2i2i−2i2i00002-22-200000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000-2200002i−2i0000
χ652-2-22-222-22-222-2-2-2-22-222000000002-2-220000-222-2000000002-2-222-2-22000000000000000000000000002i−2i00002i−2i000000
χ662-2-22-222-22-222-2-2-2-22-222000000002-2-220000-222-2000000002-2-222-2-2200000000000000000000000000−2i2i0000−2i2i000000
χ672-2-22-222-22-222-2-2-2-22-22200000000-222-20000-222-200000000-222-2-222-2000000000000000000000000002i−2i0000−2i2i000000
χ682-2-22-222-22-222-2-2-2-22-22200000000-222-20000-222-200000000-222-2-222-200000000000000000000000000−2i2i00002i−2i000000
χ69444-4-44-4-44000044-4-4-44-4004-4000000004-44-4000000000000000000000000000000000000000000000000000000000000
χ70444-4-44-4-44000044-4-4-44-400-4400000000-44-44000000000000000000000000000000000000000000000000000000000000
χ71444-4-44-4-4-20000-2-2222-22004-400000000-22-22000023−2323−2323−2323−23000000000000000000000000000000000000000000000000
χ72444-4-44-4-4-20000-2-2222-22004-400000000-22-220000−2323−2323−2323−2323000000000000000000000000000000000000000000000000
χ73444-4-44-4-4-20000-2-2222-2200-44000000002-22-2000023−2323−23−2323−2323000000000000000000000000000000000000000000000000
χ74444-4-44-4-4-20000-2-2222-2200-44000000002-22-20000−2323−232323−2323−23000000000000000000000000000000000000000000000000
χ7544-4-4-4-444400004-44-4-4-440000004-400000000000000004-4-44000000000000000000000000000000000000000000000000
χ7644-4-4-4-444400004-44-4-4-44000000-440000000000000000-444-4000000000000000000000000000000000000000000000000
χ7744-4-4-4-444-20000-22-2222-20000004-4000023−23−23230000−232323−23-222-2000000000000000000000000000000000000000000000000
χ7844-4-4-4-444-20000-22-2222-20000004-40000−232323−23000023−23−2323-222-2000000000000000000000000000000000000000000000000
χ7944-4-4-4-444-20000-22-2222-2000000-44000023−23−2323000023−23−23232-2-22000000000000000000000000000000000000000000000000
χ8044-4-4-4-444-20000-22-2222-2000000-440000−232323−230000−232323−232-2-22000000000000000000000000000000000000000000000000
χ814-444-4-4-444-44-44-4444-4-4-40000000000000000-44-4400000000000000000000000000000000000000000000000000000000
χ824-444-4-4-44-24-44-42-2-2-2222000000004i−4i4i−4i0000-22-2200000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000
χ834-444-4-4-44-24-44-42-2-2-222200000000−4i4i−4i4i0000-22-22000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000
χ844-444-4-4-44-2-44-442-2-2-222200000000000000002-22-20000000023−2323−23−2323−23230000000000000000000000000000000000000000
χ854-444-4-4-44-2-44-442-2-2-222200000000000000002-22-200000000−2323−232323−2323−230000000000000000000000000000000000000000
χ864-44-44-44-440000-44-4-44-44000000000000000000000000000000000000000000000000000000000000000000000000−2i22i200
χ874-44-44-44-440000-44-4-44-440000000000000000000000000000000000000000000000000000000000000000000000002i2−2i200
χ884-4-44-444-444-4-44-4-4-44-44400000000000000004-4-4400000000000000000000000000000000000000000000000000000000
χ894-4-44-444-4-24-4-44222-22-2-20000000000000000-222-200000000−2i32i32i3−2i32i3−2i3−2i32i30000000000000000000000000000000000000000
χ904-4-44-444-4-24-4-44222-22-2-20000000000000000-222-2000000002i3−2i3−2i32i3−2i32i32i3−2i30000000000000000000000000000000000000000
χ914-4-44-444-4-2-444-4222-22-2-2000000004-4-4400002-2-2200000000-222-2-222-20000000000000000000000000000000000000000
χ924-4-44-444-4-2-444-4222-22-2-200000000-444-400002-2-22000000002-2-222-2-220000000000000000000000000000000000000000
χ934-4-4-444-4440000-4-44-444-400000000000000000000000000000000000000000000000000000000000000000022−2200000000
χ944-4-4-444-4440000-4-44-444-4000000000000000000000000000000000000000000000000000000000000000000−222200000000
χ958-88-88-88-8-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000000000000000
χ968-8-8-888-88-4000044-44-4-440000000000000000000000000000000000000000000000000000000000000000000000000000

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