Finite Group Databasebeta

← Group #10858057

Character table — Group #10858057

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222444444444444444444444444444444444444888888888888888888888888882424242424242424242424244848
order122222223444466666662244444444441212121212121212121212121212121212121212121212122244444466666612121212121212121212121244448888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111
χ41111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1
χ5111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1111111-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ911111111111111111111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-11-1
χ1011111111111111111111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111-11
χ1111111111111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-111111-1
χ1211111111111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-1111111-1-1-1-1-1-11111-1-1111111-1-1-1-1-11
χ1311111111111111111111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111111111111111-1-1-11-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-111-11
χ1411111111111111111111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111111111111111-1-1-11-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-11-1
χ1511111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1-11
χ1611111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-1111-1
χ17222222222-2-2-2-2222222222-2-222-2-200002222-2-2-2-2-2-2-2-2-2-2-2-20000000000-200200220000-2-2000022000000000000000000
χ18222222222-2-2-2-2222222222-2-2-2-2220000-2-2-2-2-2-2-2-2-2-2-2-222220000000000200-200220000220000-2-2000000000000000000
χ19222222222-2-2-2-22222222-2-222222200002222-2-2-2-2222222220000000000-200-200-2-20000-2-20000-2-2000000000000000000
χ20222222222-2-2-2-22222222-2-222-2-2-2-20000-2-2-2-2-2-2-2-22222-2-2-2-20000000000200200-2-2000022000022000000000000000000
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
χ2222222222-12222-1-1-1-1-1-1-122222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-2-22-2-22-2-2-1-11111-1-11111-1-1111100000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-222221111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-2-2-2-2-2-222-1-1111111111111-1-1-1-100000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-21111-1-1-1-1-1-1-1-111111111111122-222-2-2-2-1-1-1-1-1-111-1-1-1-111111100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-22222-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-2-2222-2-2-2111111-1-1-1-1-1-111111100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111222-2-2-22211-1-1-1-1-1-1111111-1-1-1-100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-22222221111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-122-2-2-22-2-211-1-1-1-1111111-1-1111100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-222-2-2-2-21111-1-1-1-11111-1-1-1-111111111-2-2-22222211111111-1-1-1-1-1-1-1-1-1-100000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-122-2-222-2-20000-1-1-1-1111111111111−i3−i3−i3−i3i3i3i3i300-200200-1-1−i3−i3i3i311−i3−i3i3i3-1-1−i3−i3i3i300000000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-122-2-222-2-20000-1-1-1-1111111111111i3i3i3i3−i3−i3−i3−i300-200200-1-1i3i3−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−i3i3i3i3i300200-200-1-1i3i3−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−i300200-200-1-1−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−i3i3i3i3i300-200-20011i3i3−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−i300-200-20011−i3−i3i3i311i3i3−i3−i311−i3−i3i3i300000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-2-2-2000011111111-1-1-1-11111−i3−i3−i3−i3i3i3i3i30020020011−i3−i3i3i3-1-1i3i3−i3−i3-1-1i3i3−i3−i300000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-2-2-2000011111111-1-1-1-11111i3i3i3i3−i3−i3−i3−i30020020011i3i3−i3−i3-1-1−i3−i3i3i3-1-1−i3−i3i3i300000000000000
χ3722-222-2-2-2222-2-22-2-222-2-22-22-200000000000022-2-222-2-20000000000002-202-20002-22-22-2002-22-200000000000000000000
χ3822-222-2-2-2222-2-22-2-222-2-22-22-200000000000022-2-222-2-2000000000000-220-220002-2-22-2200-22-2200000000000000000000
χ3922-222-2-2-2222-2-22-2-222-2-2-22-2200000000000022-2-2-2-2220000000000002-20-22000-222-22-200-22-2200000000000000000000
χ4022-222-2-2-2222-2-22-2-222-2-2-22-2200000000000022-2-2-2-222000000000000-2202-2000-22-22-22002-22-200000000000000000000
χ4122-222-2-2-22-2-2222-2-222-2-22-2-2200002i2i−2i−2i0000-2-222-2-22200002i2i−2i−2i2i2i−2i−2i0000002i−2i2-20000000000002i−2i2i−2i00000000000000
χ4222-222-2-2-22-2-2222-2-222-2-22-2-220000−2i−2i2i2i0000-2-222-2-2220000−2i−2i2i2i−2i−2i2i2i000000−2i2i2-2000000000000−2i2i−2i2i00000000000000
χ4322-222-2-2-22-2-2222-2-222-2-2-222-200002i2i−2i−2i0000-2-22222-2-200002i2i−2i−2i2i2i−2i−2i000000−2i2i-22000000000000−2i2i−2i2i00000000000000
χ4422-222-2-2-22-2-2222-2-222-2-2-222-20000−2i−2i2i2i0000-2-22222-2-20000−2i−2i2i2i−2i−2i2i2i0000002i−2i-220000000000002i−2i2i−2i00000000000000
χ4522-222-2-2-2-122-2-2-111-1-1112-22-20000000033−3−3-1-111-1-11133−3−333−3−3−3−3332-202-2000-11-11-113−3-11-113−33−3−3300000000000000
χ4622-222-2-2-2-122-2-2-111-1-1112-22-20000000033−3−3-1-111-1-11133−3−3−3−33333−3−3-220-22000-111-11-13−31-11-13−3−333−300000000000000
χ4722-222-2-2-2-122-2-2-111-1-1112-22-200000000−3−333-1-111-1-111−3−33333−3−3−3−333-220-22000-111-11-1−331-11-1−333−3−3300000000000000
χ4822-222-2-2-2-122-2-2-111-1-1112-22-200000000−3−333-1-111-1-111−3−333−3−33333−3−32-202-2000-11-11-11−33-11-11−33−333−300000000000000
χ4922-222-2-2-2-122-2-2-111-1-111-22-220000000033−3−3-1-11111-1-1−3−33333−3−3−3−333-2202-20001-11-11-13−3-11-11−33−333−300000000000000
χ5022-222-2-2-2-122-2-2-111-1-111-22-220000000033−3−3-1-11111-1-1−3−333−3−33333−3−32-20-220001-1-11-113−31-11-1−333−3−3300000000000000
χ5122-222-2-2-2-122-2-2-111-1-111-22-2200000000−3−333-1-11111-1-133−3−333−3−3−3−3332-20-220001-1-11-11−331-11-13−3−333−300000000000000
χ5222-222-2-2-2-122-2-2-111-1-111-22-2200000000−3−333-1-11111-1-133−3−3−3−33333−3−3-2202-20001-11-11-1−33-11-113−33−3−3300000000000000
χ5322-222-2-2-2-1-2-222-111-1-1112-2-2200002i2i−2i−2i33−3−311-1-111-1-1−3−333−i−iii−i−iii0000002i−2i-11−i3i3i3−i3−33−i3i3i3−i33−3−ii−ii00000000000000
χ5422-222-2-2-2-1-2-222-111-1-1112-2-2200002i2i−2i−2i−3−33311-1-111-1-133−3−3−i−iii−i−iii0000002i−2i-11i3−i3−i3i33−3i3−i3−i3i3−33−ii−ii00000000000000
χ5522-222-2-2-2-1-2-222-111-1-1112-2-220000−2i−2i2i2i33−3−311-1-111-1-1−3−333ii−i−iii−i−i000000−2i2i-11i3−i3−i3i3−33i3−i3−i3i33−3i−ii−i00000000000000
χ5622-222-2-2-2-1-2-222-111-1-1112-2-220000−2i−2i2i2i−3−33311-1-111-1-133−3−3ii−i−iii−i−i000000−2i2i-11−i3i3i3−i33−3−i3i3i3−i3−33i−ii−i00000000000000
χ5722-222-2-2-2-1-2-222-111-1-111-222-200002i2i−2i−2i33−3−311-1-1-1-11133−3−3−i−iii−i−iii000000−2i2i1-1i3−i3−i3i3−33−i3i3i3−i3−33i−ii−i00000000000000
χ5822-222-2-2-2-1-2-222-111-1-111-222-200002i2i−2i−2i−3−33311-1-1-1-111−3−333−i−iii−i−iii000000−2i2i1-1−i3i3i3−i33−3i3−i3−i3i33−3i−ii−i00000000000000
χ5922-222-2-2-2-1-2-222-111-1-111-222-20000−2i−2i2i2i33−3−311-1-1-1-11133−3−3ii−i−iii−i−i0000002i−2i1-1−i3i3i3−i3−33i3−i3−i3i3−33−ii−ii00000000000000
χ6022-222-2-2-2-1-2-222-111-1-111-222-20000−2i−2i2i2i−3−33311-1-1-1-111−3−333ii−i−iii−i−i0000002i−2i1-1i3−i3−i3i33−3−i3i3i3−i33−3−ii−ii00000000000000
χ612-222-22-2-222-2-22-2222-2-2-2000000002i−2i2i−2i00002-22-2000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000002i−2i00002-20000
χ622-222-22-2-222-2-22-2222-2-2-2000000002i−2i2i−2i00002-22-2000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000−2i2i0000-220000
χ632-222-22-2-222-2-22-2222-2-2-200000000−2i2i−2i2i00002-22-200000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000002i−2i0000-220000
χ642-222-22-2-222-2-22-2222-2-2-200000000−2i2i−2i2i00002-22-200000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000−2i2i00002-20000
χ652-2-22-2-2222-22-22-2-2-22-222000000002-2-220000-222-2000000002-2-222-2-22000000000000000000000000002-200002-2000000
χ662-2-22-2-2222-22-22-2-2-22-222000000002-2-220000-222-2000000002-2-222-2-2200000000000000000000000000-220000-22000000
χ672-2-22-2-2222-22-22-2-2-22-22200000000-222-20000-222-200000000-222-2-222-2000000000000000000000000002-20000-22000000
χ682-2-22-2-2222-22-22-2-2-22-22200000000-222-20000-222-200000000-222-2-222-200000000000000000000000000-2200002-2000000
χ69444-4-4-4-444000044-4-4-44-400004i−4i0000004i−4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ70444-4-4-4-444000044-4-4-44-40000−4i4i000000−4i4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ71444-4-4-4-44-20000-2-2222-2200004i−4i000000−2i2i−2i2i000023−2323−23−2i32i3−2i32i3000000000000000000000000000000000000000000000000
χ72444-4-4-4-44-20000-2-2222-2200004i−4i000000−2i2i−2i2i0000−2323−23232i3−2i32i3−2i3000000000000000000000000000000000000000000000000
χ73444-4-4-4-44-20000-2-2222-220000−4i4i0000002i−2i2i−2i000023−2323−232i3−2i32i3−2i3000000000000000000000000000000000000000000000000
χ74444-4-4-4-44-20000-2-2222-220000−4i4i0000002i−2i2i−2i0000−2323−2323−2i32i3−2i32i3000000000000000000000000000000000000000000000000
χ7544-4-4-444-4400004-44-4-4-440000004i−4i00000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ7644-4-4-444-4400004-44-4-4-44000000−4i4i0000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ7744-4-4-444-4-20000-22-2222-20000004i−4i0000−2i32i32i3−2i30000−232323−23−2i2i2i−2i000000000000000000000000000000000000000000000000
χ7844-4-4-444-4-20000-22-2222-20000004i−4i00002i3−2i3−2i32i3000023−23−2323−2i2i2i−2i000000000000000000000000000000000000000000000000
χ7944-4-4-444-4-20000-22-2222-2000000−4i4i0000−2i32i32i3−2i3000023−23−23232i−2i−2i2i000000000000000000000000000000000000000000000000
χ8044-4-4-444-4-20000-22-2222-2000000−4i4i00002i3−2i3−2i32i30000−232323−232i−2i−2i2i000000000000000000000000000000000000000000000000
χ814-444-44-4-44-444-4-4444-4-4-40000000000000000-44-4400000000000000000000000000000000000000000000000000000000
χ824-444-44-4-4-24-4-442-2-2-2222000000004i−4i4i−4i0000-22-2200000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000
χ834-444-44-4-4-24-4-442-2-2-222200000000−4i4i−4i4i0000-22-22000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000
χ844-444-44-4-4-2-444-42-2-2-222200000000000000002-22-20000000023−2323−23−2323−23230000000000000000000000000000000000000000
χ854-444-44-4-4-2-444-42-2-2-222200000000000000002-22-200000000−2323−232323−2323−230000000000000000000000000000000000000000
χ864-44-44-44-440000-44-4-44-44000000000000000000000000000000000000000000000000000000000000000000000000−2i22i200
χ874-44-44-44-440000-44-4-44-440000000000000000000000000000000000000000000000000000000000000000000000002i2−2i200
χ884-4-44-4-44444-44-4-4-4-44-44400000000000000004-4-4400000000000000000000000000000000000000000000000000000000
χ894-4-44-4-444-24-44-4222-22-2-20000000000000000-222-200000000−2i32i32i3−2i32i3−2i3−2i32i30000000000000000000000000000000000000000
χ904-4-44-4-444-24-44-4222-22-2-20000000000000000-222-2000000002i3−2i3−2i32i3−2i32i32i3−2i30000000000000000000000000000000000000000
χ914-4-44-4-444-2-44-44222-22-2-2000000004-4-4400002-2-2200000000-222-2-222-20000000000000000000000000000000000000000
χ924-4-44-4-444-2-44-44222-22-2-200000000-444-400002-2-22000000002-2-222-2-220000000000000000000000000000000000000000
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).