Finite Group Databasebeta

← Group #10858972

Character table — Group #10858972

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222444444444444444444444444444444444444888888888888888888888888882424242424242424242424244848
order1222222234444666666622444444444466661212121212121212121212121212121212121212224444446666121212121212121212121212121244448888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11111-1-1-1-1
χ41111111111111111111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111
χ5111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ6111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1111111-1-1-1-111-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111
χ911111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-11-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-11
χ1011111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-11-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11-1
χ1111111111111111111111-1-1-1-11111-1-111-1-1-1-11111111111111111-1-1-1-1-1-111-1-1-11-1-1-1-1-1-111-1-11111-1-1-1-111-1-11111-1-1-1-11-1
χ1211111111111111111111-1-1-1-11111-1-111-1-1-1-11111111111111111-1-1-1-1-1-111-1-1-11-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-11111-11
χ1311111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111111-1-1-1-1-111-1-1-1-11111111111-1-111-1-111-1-1-11
χ1411111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111111-1-1-1-1-111-1-1-1-111111111-1-111-1-111-1-1111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-111111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-111111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-111111-1-111-1-1-1-1-1-11111-1-1111111-1-1-1-1-11
χ17222222222-2-2-2-2222222222-2-20000222222222222-2-2-2-2000000002222000000-2-20000-2-2-2-2-2-20000000000000000000000
χ18222222222-2-2-2-2222222222-2-20000-2-2-2-22222-2-2-2-2-2-2-2-200000000-2-2-2-20000002200002222-2-20000000000000000000000
χ19222222222-2-2-2-22222222-2-222000022-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000002222000000-220000-2-222220000000000000000000000
χ20222222222-2-2-2-22222222-2-2220000-2-222-2-2-2-22222-2-2-2-200000000-2-2-2-20000002-2000022-2-2220000000000000000000000
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
χ2222222222-12222-1-1-1-1-1-1-122222222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-2-2-2-222-2-211111111-1-11111-1-1-1-100000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-2-2-2-2-2-2221111-1-1-1-1-1-11111111100000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-11111-1-1-1-11111111111112222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1111100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2222222-2-211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-22-2-1-1-1-1-1-111111111111100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2221111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-2-222-2-2-22111111-1-111-1-1-1-1111100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222-2-211111111-1-1-1-111111111-1-1-1-1-2-222222-21111-1-11111-1-1-1-1-1-1-1-100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2221111-1-1-1-1-1-1-1-111111111111122-2-222-22-1-1-1-111-1-1111111-1-1-1-100000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-122-2-200002222-1-1-1-1-1-1-1-11111−i3−i3−i3−i3i3i3i3i3-1-1-1-1000000-2-2−i3−i3i3i3111111−i3−i3i3i3−i3−i3i3i300000000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-122-2-200002222-1-1-1-1-1-1-1-11111i3i3i3i3−i3−i3−i3−i3-1-1-1-1000000-2-2i3i3−i3−i3111111i3i3−i3−i3i3i3−i3−i300000000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-122-2-20000-2-2-2-2-1-1-1-111111111−i3−i3−i3−i3i3i3i3i3111100000022i3i3−i3−i3-1-1-1-111i3i3−i3−i3−i3−i3i3i300000000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-122-2-20000-2-2-2-2-1-1-1-111111111i3i3i3i3−i3−i3−i3−i3111100000022−i3−i3i3i3-1-1-1-111−i3−i3i3i3i3i3−i3−i300000000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222000022-2-2111111111111−i3−i3−i3−i3i3i3i3i3-1-1-1-1000000-22−i3−i3i3i311-1-1-1-1i3i3−i3−i3i3i3−i3−i300000000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222000022-2-2111111111111i3i3i3i3−i3−i3−i3−i3-1-1-1-1000000-22i3i3−i3−i311-1-1-1-1−i3−i3i3i3−i3−i3i3i300000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2220000-2-2221111-1-1-1-11111−i3−i3−i3−i3i3i3i3i311110000002-2i3i3−i3−i3-1-111-1-1−i3−i3i3i3i3i3−i3−i300000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2220000-2-2221111-1-1-1-11111i3i3i3i3−i3−i3−i3−i311110000002-2−i3−i3i3i3-1-111-1-1i3i3−i3−i3−i3−i3i3i300000000000000
χ372222-2-2-2-2222-2-22-2-2-222-22-22-20000000022-2-2000022-2-20000000000002-22-200002-22-200002-22-22-2000000000000000000
χ382222-2-2-2-2222-2-22-2-2-222-22-22-20000000022-2-2000022-2-2000000000000-22-220000-22-2200002-2-22-22000000000000000000
χ392222-2-2-2-2222-2-22-2-2-222-2-22-2200000000-2-222000022-2-20000000000002-2-2200002-22-20000-22-22-22000000000000000000
χ402222-2-2-2-2222-2-22-2-2-222-2-22-2200000000-2-222000022-2-2000000000000-222-20000-22-220000-222-22-2000000000000000000
χ412222-2-2-2-22-2-2222-2-2-222-22-2-222i2i−2i−2i000022-2-20000-2-2222i2i−2i−2i2i2i−2i−2i000000002i−2i0000000000-2200002i−2i2i−2i00000000000000
χ422222-2-2-2-22-2-2222-2-2-222-22-2-22−2i−2i2i2i000022-2-20000-2-222−2i−2i2i2i−2i−2i2i2i00000000−2i2i0000000000-220000−2i2i−2i2i00000000000000
χ432222-2-2-2-22-2-2222-2-2-222-2-222-22i2i−2i−2i0000-2-2220000-2-2222i2i−2i−2i2i2i−2i−2i00000000−2i2i00000000002-20000−2i2i−2i2i00000000000000
χ442222-2-2-2-22-2-2222-2-2-222-2-222-2−2i−2i2i2i0000-2-2220000-2-222−2i−2i2i2i−2i−2i2i2i000000002i−2i00000000002-200002i−2i2i−2i00000000000000
χ452222-2-2-2-2-122-2-2-1111-1-112-22-200000000-1-11133−3−3-1-11133−3−3−3−33333−3−32-22-20000-11-113−33−3-11-11-113−3−3300000000000000
χ462222-2-2-2-2-122-2-2-1111-1-112-22-200000000-1-11133−3−3-1-111−3−33333−3−333−3−3-22-2200001-11-13−33−3-111-11-1−333−300000000000000
χ472222-2-2-2-2-122-2-2-1111-1-112-22-200000000-1-111−3−333-1-11133−3−3−3−333−3−333-22-2200001-11-1−33−33-111-11-13−3−3300000000000000
χ482222-2-2-2-2-122-2-2-1111-1-112-22-200000000-1-111−3−333-1-111−3−33333−3−3−3−3332-22-20000-11-11−33−33-11-11-11−333−300000000000000
χ492222-2-2-2-2-122-2-2-1111-1-11-22-220000000011-1-133−3−3-1-11133−3−3−3−333−3−333-222-200001-11-1−333−31-1-11-11−333−300000000000000
χ502222-2-2-2-2-122-2-2-1111-1-11-22-220000000011-1-133−3−3-1-111−3−33333−3−3−3−3332-2-220000-11-11−333−31-11-11-13−3−3300000000000000
χ512222-2-2-2-2-122-2-2-1111-1-11-22-220000000011-1-1−3−333-1-11133−3−3−3−33333−3−32-2-220000-11-113−3−331-11-11-1−333−300000000000000
χ522222-2-2-2-2-122-2-2-1111-1-11-22-220000000011-1-1−3−333-1-111−3−33333−3−333−3−3-222-200001-11-13−3−331-1-11-113−3−3300000000000000
χ532222-2-2-2-2-1-2-222-1111-1-112-2-222i2i−2i−2i0000-1-11133−3−311-1-1−i−iii−i−iii33−3−300002i−2i00−i3i3i3−i3−33−331-1−i3i3i3−i3−ii−ii00000000000000
χ542222-2-2-2-2-1-2-222-1111-1-112-2-222i2i−2i−2i0000-1-111−3−33311-1-1−i−iii−i−iii−3−33300002i−2i00i3−i3−i3i33−33−31-1i3−i3−i3i3−ii−ii00000000000000
χ552222-2-2-2-2-1-2-222-1111-1-112-2-22−2i−2i2i2i0000-1-11133−3−311-1-1ii−i−iii−i−i33−3−30000−2i2i00i3−i3−i3i3−33−331-1i3−i3−i3i3i−ii−i00000000000000
χ562222-2-2-2-2-1-2-222-1111-1-112-2-22−2i−2i2i2i0000-1-111−3−33311-1-1ii−i−iii−i−i−3−3330000−2i2i00−i3i3i3−i33−33−31-1−i3i3i3−i3i−ii−i00000000000000
χ572222-2-2-2-2-1-2-222-1111-1-11-222-22i2i−2i−2i000011-1-133−3−311-1-1−i−iii−i−iii−3−3330000−2i2i00i3−i3−i3i33−3−33-11−i3i3i3−i3i−ii−i00000000000000
χ582222-2-2-2-2-1-2-222-1111-1-11-222-22i2i−2i−2i000011-1-1−3−33311-1-1−i−iii−i−iii33−3−30000−2i2i00−i3i3i3−i3−333−3-11i3−i3−i3i3i−ii−i00000000000000
χ592222-2-2-2-2-1-2-222-1111-1-11-222-2−2i−2i2i2i000011-1-133−3−311-1-1ii−i−iii−i−i−3−33300002i−2i00−i3i3i3−i33−3−33-11i3−i3−i3i3−ii−ii00000000000000
χ602222-2-2-2-2-1-2-222-1111-1-11-222-2−2i−2i2i2i000011-1-1−3−33311-1-1ii−i−iii−i−i33−3−300002i−2i00i3−i3−i3i3−333−3-11−i3i3i3−i3−ii−ii00000000000000
χ612-22-222-2-222-22-2-22-2-22-2200002-22-20000000000002-22-22-22-22-22-20000000000000000000000000000002i−2i00002i−2i000000
χ622-22-222-2-222-22-2-22-2-22-2200002-22-20000000000002-22-22-22-22-22-2000000000000000000000000000000−2i2i0000−2i2i000000
χ632-22-222-2-222-22-2-22-2-22-220000-22-220000000000002-22-2-22-22-22-220000000000000000000000000000002i−2i0000−2i2i000000
χ642-22-222-2-222-22-2-22-2-22-220000-22-220000000000002-22-2-22-22-22-22000000000000000000000000000000−2i2i00002i−2i000000
χ652-22-2-2-2222-222-2-2-2222-2-200002i−2i−2i2i000000000000-222-22i−2i−2i2i2i−2i−2i2i000000000000000000000000000000002-200002i−2i0000
χ662-22-2-2-2222-222-2-2-2222-2-200002i−2i−2i2i000000000000-222-22i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000-220000−2i2i0000
χ672-22-2-2-2222-222-2-2-2222-2-20000−2i2i2i−2i000000000000-222-2−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000002-20000−2i2i0000
χ682-22-2-2-2222-222-2-2-2222-2-20000−2i2i2i−2i000000000000-222-2−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000-2200002i−2i0000
χ6944-4-44-44-4400004-44-4-4-44000000000000000000000000000000000000000000000000000000000000000000−2i22i200000000
χ7044-4-44-44-4400004-44-4-4-440000000000000000000000000000000000000000000000000000000000000000002i2−2i200000000
χ7144-4-4-44-444000044-44-4-4-4000000000000000000000000000000000000000000000000000000000000000000000000−2i22i200
χ7244-4-4-44-444000044-44-4-4-40000000000000000000000000000000000000000000000000000000000000000000000002i2−2i200
χ734-44-444-4-44-44-44-44-4-44-4400000000000000000000-44-440000000000000000000000000000000000000000000000000000
χ744-44-444-4-4-24-44-42-222-22-200004-44-4000000000000-22-22-22-22-22-2200000000000000000000000000000000000000000000
χ754-44-444-4-4-24-44-42-222-22-20000-44-44000000000000-22-222-22-22-22-200000000000000000000000000000000000000000000
χ764-44-444-4-4-2-44-442-222-22-2000000000000000000002-22-2−2i32i3−2i32i32i3−2i32i3−2i300000000000000000000000000000000000000000000
χ774-44-444-4-4-2-44-442-222-22-2000000000000000000002-22-22i3−2i32i3−2i3−2i32i3−2i32i300000000000000000000000000000000000000000000
χ784-44-4-4-44444-4-44-4-4444-4-4000000000000000000004-4-440000000000000000000000000000000000000000000000000000
χ794-44-4-4-444-24-4-4422-2-2-22200000000000000000000-222-223−23−2323−232323−2300000000000000000000000000000000000000000000
χ804-44-4-4-444-24-4-4422-2-2-22200000000000000000000-222-2−232323−2323−23−232300000000000000000000000000000000000000000000
χ814-44-4-4-444-2-444-422-2-2-22200004i−4i−4i4i0000000000002-2-22−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000000000000000
χ824-44-4-4-444-2-444-422-2-2-2220000−4i4i4i−4i0000000000002-2-222i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000000000000000
χ834-4-444-4-4440000-4-4-44-44400000000004-400004-44-400000000000000000000000000000000000000000000000000000000
χ844-4-444-4-4440000-4-4-44-4440000000000-440000-44-4400000000000000000000000000000000000000000000000000000000
χ854-4-444-4-44-20000222-22-2-200000000004-4−2i32i3−2i32i3-22-22000000000000−2i32i3−2i32i30000000000000000000000000000000000000000
χ864-4-444-4-44-20000222-22-2-200000000004-42i3−2i32i3−2i3-22-220000000000002i3−2i32i3−2i30000000000000000000000000000000000000000
χ874-4-444-4-44-20000222-22-2-20000000000-44−2i32i3−2i32i32-22-20000000000002i3−2i32i3−2i30000000000000000000000000000000000000000
χ884-4-444-4-44-20000222-22-2-20000000000-442i3−2i32i3−2i32-22-2000000000000−2i32i3−2i32i30000000000000000000000000000000000000000
χ894-4-44-444-440000-444-4-44-4000000004i−4i00000000000000000000004i−4i−4i4i0000000000000000000000000000000000000000
χ904-4-44-444-440000-444-4-44-400000000−4i4i0000000000000000000000−4i4i4i−4i0000000000000000000000000000000000000000
χ914-4-44-444-4-200002-2-222-22000000004i−4i00−2i32i32i3−2i323−23−2323000000000000−2i2i2i−2i0000000000000000000000000000000000000000
χ924-4-44-444-4-200002-2-222-22000000004i−4i002i3−2i3−2i32i3−232323−23000000000000−2i2i2i−2i0000000000000000000000000000000000000000
χ934-4-44-444-4-200002-2-222-2200000000−4i4i00−2i32i32i3−2i3−232323−230000000000002i−2i−2i2i0000000000000000000000000000000000000000
χ944-4-44-444-4-200002-2-222-2200000000−4i4i002i3−2i3−2i32i323−23−23230000000000002i−2i−2i2i0000000000000000000000000000000000000000
χ9588-8-88-88-8-40000-44-4444-40000000000000000000000000000000000000000000000000000000000000000000000000000
χ9688-8-8-88-88-40000-4-44-44440000000000000000000000000000000000000000000000000000000000000000000000000000

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