Finite Group Databasebeta

← Group #10858102

Character table — Group #10858102

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222444444444444444444444444444444444444888888888888888888888888882424242424242424242424244848
order1222222234444666666622444444444466661212121212121212121212121212121212121212224444446666121212121212121212121212121244448888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ41111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ5111111111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-11111-1-1-1-1111111-1-1-1-1111111-1-1-1-111-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111
χ911111111111111111111-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-111111111-1-1111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11-1
χ1011111111111111111111-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-111111111-1-1111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-11
χ1111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111-1
χ1211111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-11
χ1311111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-11
χ1411111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11-1
χ1511111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-111-1-11111111111-1-111-1-111-1-1-11
χ1611111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-111-1-111111111-1-111-1-111-1-1111-1
χ17222222222-2-2-2-2222222222-2-22222000022222222-2-2-2-222220000000000-20000-20000-2-2-2-2-2-20000000000000000000000
χ18222222222-2-2-2-2222222222-2-2-2-2-2-200002222-2-2-2-2-2-2-2-2-2-2-2-2000000000020000200002222-2-20000000000000000000000
χ19222222222-2-2-2-22222222-2-22222-2-20000-2-2-2-22222-2-2-2-2-2-2-2-20000000000-2000020000-2-222220000000000000000000000
χ20222222222-2-2-2-22222222-2-222-2-2220000-2-2-2-2-2-2-2-2-2-2-2-22222000000000020000-2000022-2-2220000000000000000000000
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
χ2222222222-12222-1-1-1-1-1-1-122222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-2-22-2-2-2-221111-1-1-1-1-1-11111111100000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-22222-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-2-2-2-2-222-211111111-1-11111-1-1-1-100000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-11111-1-1-1-111111111111122-222-2-2-2-1-1-1-11111-1-1-1-1-1-1111100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-222221111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-2-2222-2-2-21111-1-11111-1-1-1-1111100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-2-21111-1-1-1-1-1-1-1-1111111111111222-2-222-2-1-1-1-1-1-111111111-1-1-1-100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-222222211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-22-1-1-1-111-1-1111111111100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-222-2-2-2-211111111-1-1-1-1-1-1-1-111111111-2-2-222222111111-1-111-1-1-1-1-1-1-1-100000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-122-2-222220000-1-1-1-1-1-1-1-11111-1-1-1-1−i3−i3−i3−i3i3i3i3i300-20000-2−i3−i3i3i3111111−i3−i3i3i3−i3−i3i3i300000000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-122-2-222220000-1-1-1-1-1-1-1-11111-1-1-1-1i3i3i3i3−i3−i3−i3−i300-20000-2i3i3−i3−i3111111i3i3−i3−i3i3i3−i3−i300000000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-2-2-20000-1-1-1-1111111111111−i3−i3−i3−i3i3i3i3i300200002i3i3−i3−i3-1-1-1-111i3i3−i3−i3−i3−i3i3i300000000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-2-2-20000-1-1-1-1111111111111i3i3i3i3−i3−i3−i3−i300200002−i3−i3i3i3-1-1-1-111−i3−i3i3i3i3i3−i3−i300000000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-200001111-1-1-1-111111111−i3−i3−i3−i3i3i3i3i300-200002i3i3−i3−i311-1-1-1-1−i3−i3i3i3i3i3−i3−i300000000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-200001111-1-1-1-111111111i3i3i3i3−i3−i3−i3−i300-200002−i3−i3i3i311-1-1-1-1i3i3−i3−i3−i3−i3i3i300000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-2220000111111111111-1-1-1-1−i3−i3−i3−i3i3i3i3i30020000-2−i3−i3i3i3-1-111-1-1i3i3−i3−i3i3i3−i3−i300000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-2220000111111111111-1-1-1-1i3i3i3i3−i3−i3−i3−i30020000-2i3i3−i3−i3-1-111-1-1−i3−i3i3i3−i3−i3i3i300000000000000
χ3722-222-2-2-2222-2-22-2-2-222-22-22-20000000022-2-2000022-2-20000000000002-202-20002-22-200002-22-22-2000000000000000000
χ3822-222-2-2-2222-2-22-2-2-222-22-22-20000000022-2-2000022-2-2000000000000-220-22000-22-2200002-2-22-22000000000000000000
χ3922-222-2-2-2222-2-22-2-2-222-2-22-2200000000-2-222000022-2-20000000000002-20-220002-22-20000-22-22-22000000000000000000
χ4022-222-2-2-2222-2-22-2-2-222-2-22-2200000000-2-222000022-2-2000000000000-2202-2000-22-220000-222-22-2000000000000000000
χ4122-222-2-2-22-2-2222-2-2-222-22-2-2200002i2i−2i−2i22-2-20000-2-22200002i2i−2i−2i2i2i−2i−2i000002i−2i000000000-2200002i−2i2i−2i00000000000000
χ4222-222-2-2-22-2-2222-2-2-222-22-2-220000−2i−2i2i2i22-2-20000-2-2220000−2i−2i2i2i−2i−2i2i2i00000−2i2i000000000-220000−2i2i−2i2i00000000000000
χ4322-222-2-2-22-2-2222-2-2-222-2-222-200002i2i−2i−2i-2-2220000-2-22200002i2i−2i−2i2i2i−2i−2i00000−2i2i0000000002-20000−2i2i−2i2i00000000000000
χ4422-222-2-2-22-2-2222-2-2-222-2-222-20000−2i−2i2i2i-2-2220000-2-2220000−2i−2i2i2i−2i−2i2i2i000002i−2i0000000002-200002i−2i2i−2i00000000000000
χ4522-222-2-2-2-122-2-2-1111-1-112-22-200000000-1-11133−3−3-1-11133−3−333−3−3−3−3332-202-2000-11-113−33−3-11-11-113−3−3300000000000000
χ4622-222-2-2-2-122-2-2-1111-1-112-22-200000000-1-11133−3−3-1-11133−3−3−3−33333−3−3-220-220001-11-13−33−3-111-11-1−333−300000000000000
χ4722-222-2-2-2-122-2-2-1111-1-112-22-200000000-1-111−3−333-1-111−3−33333−3−3−3−333-220-220001-11-1−33−33-111-11-13−3−3300000000000000
χ4822-222-2-2-2-122-2-2-1111-1-112-22-200000000-1-111−3−333-1-111−3−333−3−33333−3−32-202-2000-11-11−33−33-11-11-11−333−300000000000000
χ4922-222-2-2-2-122-2-2-1111-1-11-22-220000000011-1-133−3−3-1-111−3−33333−3−3−3−333-2202-20001-11-13−3−331-1-11-11−333−300000000000000
χ5022-222-2-2-2-122-2-2-1111-1-11-22-220000000011-1-133−3−3-1-111−3−333−3−33333−3−32-20-22000-11-113−3−331-11-11-13−3−3300000000000000
χ5122-222-2-2-2-122-2-2-1111-1-11-22-220000000011-1-1−3−333-1-11133−3−333−3−3−3−3332-20-22000-11-11−333−31-11-11-1−333−300000000000000
χ5222-222-2-2-2-122-2-2-1111-1-11-22-220000000011-1-1−3−333-1-11133−3−3−3−33333−3−3-2202-20001-11-1−333−31-1-11-113−3−3300000000000000
χ5322-222-2-2-2-1-2-222-1111-1-112-2-2200002i2i−2i−2i-1-11133−3−311-1-133−3−3−i−iii−i−iii000002i−2i0−i3i3i3−i3−33−331-1−i3i3i3−i3−ii−ii00000000000000
χ5422-222-2-2-2-1-2-222-1111-1-112-2-2200002i2i−2i−2i-1-111−3−33311-1-1−3−333−i−iii−i−iii000002i−2i0i3−i3−i3i33−33−31-1i3−i3−i3i3−ii−ii00000000000000
χ5522-222-2-2-2-1-2-222-1111-1-112-2-220000−2i−2i2i2i-1-11133−3−311-1-133−3−3ii−i−iii−i−i00000−2i2i0i3−i3−i3i3−33−331-1i3−i3−i3i3i−ii−i00000000000000
χ5622-222-2-2-2-1-2-222-1111-1-112-2-220000−2i−2i2i2i-1-111−3−33311-1-1−3−333ii−i−iii−i−i00000−2i2i0−i3i3i3−i33−33−31-1−i3i3i3−i3i−ii−i00000000000000
χ5722-222-2-2-2-1-2-222-1111-1-11-222-200002i2i−2i−2i11-1-133−3−311-1-1−3−333−i−iii−i−iii00000−2i2i0i3−i3−i3i3−333−3-11−i3i3i3−i3i−ii−i00000000000000
χ5822-222-2-2-2-1-2-222-1111-1-11-222-200002i2i−2i−2i11-1-1−3−33311-1-133−3−3−i−iii−i−iii00000−2i2i0−i3i3i3−i33−3−33-11i3−i3−i3i3i−ii−i00000000000000
χ5922-222-2-2-2-1-2-222-1111-1-11-222-20000−2i−2i2i2i11-1-133−3−311-1-1−3−333ii−i−iii−i−i000002i−2i0−i3i3i3−i3−333−3-11i3−i3−i3i3−ii−ii00000000000000
χ6022-222-2-2-2-1-2-222-1111-1-11-222-20000−2i−2i2i2i11-1-1−3−33311-1-133−3−3ii−i−iii−i−i000002i−2i0i3−i3−i3i33−3−33-11−i3i3i3−i3−ii−ii00000000000000
χ612-222-22-2-222-2-22-222-22-2-2000000002i−2i2i−2i000000002-22-200002i−2i2i−2i2i−2i2i−2i00000000000000000000000000002i−2i00002-20000
χ622-222-22-2-222-2-22-222-22-2-2000000002i−2i2i−2i000000002-22-200002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000−2i2i0000-220000
χ632-222-22-2-222-2-22-222-22-2-200000000−2i2i−2i2i000000002-22-20000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000002i−2i0000-220000
χ642-222-22-2-222-2-22-222-22-2-200000000−2i2i−2i2i000000002-22-20000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000−2i2i00002-20000
χ652-2-22-2-2222-22-22-2-2-222-22000000002-2-2200000000-222-200002-2-222-2-22000000000000000000000000002-200002-2000000
χ662-2-22-2-2222-22-22-2-2-222-22000000002-2-2200000000-222-200002-2-222-2-2200000000000000000000000000-220000-22000000
χ672-2-22-2-2222-22-22-2-2-222-2200000000-222-200000000-222-20000-222-2-222-2000000000000000000000000002-20000-22000000
χ682-2-22-2-2222-22-22-2-2-222-2200000000-222-200000000-222-20000-222-2-222-200000000000000000000000000-2200002-2000000
χ69444-4-4-44-44000044-4-4-4-44000000000000000000000000000000000000000000000000000000000000000000−2i22i200000000
χ70444-4-4-44-44000044-4-4-4-440000000000000000000000000000000000000000000000000000000000000000002i2−2i200000000
χ7144-4-4-44-44400004-444-4-4-4000000000000000000000000000000000000000000000000000000000000000000000000−2i22i200
χ7244-4-4-44-44400004-444-4-4-40000000000000000000000000000000000000000000000000000000000000000000000002i2−2i200
χ734-444-44-4-44-444-4-444-44-4-400000000000000000000-44-440000000000000000000000000000000000000000000000000000
χ744-444-44-4-4-24-4-442-2-22-222000000004i−4i4i−4i00000000-22-220000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000
χ754-444-44-4-4-24-4-442-2-22-22200000000−4i4i−4i4i00000000-22-2200002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000
χ764-444-44-4-4-2-444-42-2-22-222000000000000000000002-22-2000023−2323−23−2323−23230000000000000000000000000000000000000000
χ774-444-44-4-4-2-444-42-2-22-222000000000000000000002-22-20000−2323−232323−2323−230000000000000000000000000000000000000000
χ784-44-44-4-4440000-44-44-44-40000004i−4i00000000000000004i−4i4i−4i000000000000000000000000000000000000000000000000
χ794-44-44-4-4440000-44-44-44-4000000−4i4i0000000000000000−4i4i−4i4i000000000000000000000000000000000000000000000000
χ804-44-44-4-44-200002-22-22-220000004i−4i0000−2i32i3−2i32i323−2323−230000−2i2i−2i2i000000000000000000000000000000000000000000000000
χ814-44-44-4-44-200002-22-22-220000004i−4i00002i3−2i32i3−2i3−2323−23230000−2i2i−2i2i000000000000000000000000000000000000000000000000
χ824-44-44-4-44-200002-22-22-22000000−4i4i0000−2i32i3−2i32i3−2323−232300002i−2i2i−2i000000000000000000000000000000000000000000000000
χ834-44-44-4-44-200002-22-22-22000000−4i4i00002i3−2i32i3−2i323−2323−2300002i−2i2i−2i000000000000000000000000000000000000000000000000
χ844-4-44-4-44444-44-4-4-4-444-44000000000000000000004-4-440000000000000000000000000000000000000000000000000000
χ854-4-44-4-444-24-44-4222-2-22-200000000000000000000-222-20000−2i32i32i3−2i32i3−2i3−2i32i30000000000000000000000000000000000000000
χ864-4-44-4-444-24-44-4222-2-22-200000000000000000000-222-200002i3−2i3−2i32i3−2i32i32i3−2i30000000000000000000000000000000000000000
χ874-4-44-4-444-2-44-44222-2-22-2000000004-4-44000000002-2-220000-222-2-222-20000000000000000000000000000000000000000
χ884-4-44-4-444-2-44-44222-2-22-200000000-444-4000000002-2-2200002-2-222-2-220000000000000000000000000000000000000000
χ894-4-4-4444-440000-4-44-4-44400004-400000000004-4-4400000000000000000000000000000000000000000000000000000000
χ904-4-4-4444-440000-4-44-4-4440000-440000000000-444-400000000000000000000000000000000000000000000000000000000
χ914-4-4-4444-4-2000022-222-2-200004-4000000−2i32i32i3−2i3-222-20000−2i32i32i3−2i3000000000000000000000000000000000000000000000000
χ924-4-4-4444-4-2000022-222-2-200004-40000002i3−2i3−2i32i3-222-200002i3−2i3−2i32i3000000000000000000000000000000000000000000000000
χ934-4-4-4444-4-2000022-222-2-20000-44000000−2i32i32i3−2i32-2-2200002i3−2i3−2i32i3000000000000000000000000000000000000000000000000
χ944-4-4-4444-4-2000022-222-2-20000-440000002i3−2i3−2i32i32-2-220000−2i32i32i3−2i3000000000000000000000000000000000000000000000000
χ95888-8-8-88-8-40000-4-44444-40000000000000000000000000000000000000000000000000000000000000000000000000000
χ9688-8-8-88-88-40000-44-4-44440000000000000000000000000000000000000000000000000000000000000000000000000000

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