Finite Group Databasebeta

← Group #10822590

Character table — Group #10822590

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444448888888888888888888888888888888888881212121212121212242424242424242424242424
order1222444422222234444446661212121266666612121212121244444444444412121212121212121212121212121212121212121212121222224444444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ101111-1-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111
χ111111-1-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111
χ121111-1-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1
χ131111-1-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111
χ141111-1-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1
χ151111-1-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1
χ161111-1-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111
χ1722222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ1822222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000000000000000
χ1922222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-11111111100000000000000000000
χ2022222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-100000000000000000000
χ21222222222-2-22-2-2222-2-2-2-2222222222-2-2-2-222-2-2-2-2000000002-22-2000000000000000022-2-222-2-200000000000000000000
χ22222222222-2-22-2-2222-2-2-2-2222222222-2-2-2-222-2-2-2-200000000-22-220000000000000000-2-222-2-22200000000000000000000
χ23222222222-2-22-2-2-122-2-2-2-2-1-1-1-1-1-1-1-1-11111-1-11111000000002-22-2−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3-1-111-1-11100000000000000000000
χ24222222222-2-22-2-2-122-2-2-2-2-1-1-1-1-1-1-1-1-11111-1-11111000000002-22-2i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3-1-111-1-11100000000000000000000
χ25222222222-2-22-2-2-122-2-2-2-2-1-1-1-1-1-1-1-1-11111-1-1111100000000-22-22−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i311-1-111-1-100000000000000000000
χ26222222222-2-22-2-2-122-2-2-2-2-1-1-1-1-1-1-1-1-11111-1-1111100000000-22-22i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i311-1-111-1-100000000000000000000
χ2722222222-22-2-22-22-2-222-2-22222222-2-222-2-2-2-222-2-200002-22-20000000000002-22-22-22-20000000000000000000000000000
χ2822222222-22-2-22-22-2-222-2-22222222-2-222-2-2-2-222-2-20000-22-22000000000000-22-22-22-220000000000000000000000000000
χ2922222222-22-2-22-2-1-2-222-2-2-1-1-1-1-1-1-111-1-11111-1-11100002-22-20000−i3i3−i3i3−i3i3−i3i3-11-11-11-11−i3i3−i3i3−i3i3−i3i300000000000000000000
χ3022222222-22-2-22-2-1-2-222-2-2-1-1-1-1-1-1-111-1-11111-1-11100002-22-20000i3−i3i3−i3i3−i3i3−i3-11-11-11-11i3−i3i3−i3i3−i3i3−i300000000000000000000
χ3122222222-22-2-22-2-1-2-222-2-2-1-1-1-1-1-1-111-1-11111-1-1110000-22-220000−i3i3−i3i3−i3i3−i3i31-11-11-11-1i3−i3i3−i3i3−i3i3−i300000000000000000000
χ3222222222-22-2-22-2-1-2-222-2-2-1-1-1-1-1-1-111-1-11111-1-1110000-22-220000i3−i3i3−i3i3−i3i3−i31-11-11-11-1−i3i3−i3i3−i3i3−i3i300000000000000000000
χ3322222222-2-22-2-222-2-2-2-2222222222-2-2-2-222-2-2-2-2222-22-2000000002-2-222-2-22000000000000000000000000000000000000
χ3422222222-2-22-2-222-2-2-2-2222222222-2-2-2-222-2-2-2-222-22-2200000000-222-2-222-2000000000000000000000000000000000000
χ3522222222-2-22-2-22-1-2-2-2-222-1-1-1-1-1-1-11111-1-11111-1-12-22-200000000-111-1-111-1−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i300000000000000000000
χ3622222222-2-22-2-22-1-2-2-2-222-1-1-1-1-1-1-11111-1-11111-1-12-22-200000000-111-1-111-1i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i300000000000000000000
χ3722222222-2-22-2-22-1-2-2-2-222-1-1-1-1-1-1-11111-1-11111-1-1-22-22000000001-1-111-1-11−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3i3−i3−i3i300000000000000000000
χ3822222222-2-22-2-22-1-2-2-2-222-1-1-1-1-1-1-11111-1-11111-1-1-22-22000000001-1-111-1-11i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3−i3i3i3−i300000000000000000000
χ392222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-111111122-2-222-2-222-2-2-1-1-1-11111-1-1-1-11111-1-1-1-1111100000000000000000000
χ402222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-111111122-2-2-2-222-2-222-1-1-1-111111111-1-1-1-11111-1-1-1-100000000000000000000
χ412222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-1111111-2-22222-2-2-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-100000000000000000000
χ422222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-1111111-2-222-2-22222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000
χ432222-2-2-2-22-2-22-2-22-2-22222222-2-2-2-222-2-2-2-2-2-22222000000002-2-22000000000000000022-2-2-2-22200000000000000000000
χ442222-2-2-2-22-2-22-2-22-2-22222222-2-2-2-222-2-2-2-2-2-2222200000000-222-20000000000000000-2-22222-2-200000000000000000000
χ452222-2-2-2-22-2-22-2-2-1-2-22222-1-1-11111-1-1111111-1-1-1-1000000002-2-22−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3-1-11111-1-100000000000000000000
χ462222-2-2-2-22-2-22-2-2-1-2-22222-1-1-11111-1-1111111-1-1-1-1000000002-2-22i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3-1-11111-1-100000000000000000000
χ472222-2-2-2-22-2-22-2-2-1-2-22222-1-1-11111-1-1111111-1-1-1-100000000-222-2−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i311-1-1-1-11100000000000000000000
χ482222-2-2-2-22-2-22-2-2-1-2-22222-1-1-11111-1-1111111-1-1-1-100000000-222-2i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i311-1-1-1-11100000000000000000000
χ492222-2-2-2-2-22-2-22-2222-2-222222-2-2-2-2-2-222-2-222-2-22200002-2-220000000000002-22-2-22-220000000000000000000000000000
χ502222-2-2-2-2-22-2-22-2222-2-222222-2-2-2-2-2-222-2-222-2-2220000-222-2000000000000-22-222-22-20000000000000000000000000000
χ512222-2-2-2-2-22-2-22-2-122-2-222-1-1-1111111-1-111-1-111-1-100002-2-220000−i3i3−i3i3i3−i3i3−i3-11-111-11-1−i3i3−i3i3i3−i3i3−i300000000000000000000
χ522222-2-2-2-2-22-2-22-2-122-2-222-1-1-1111111-1-111-1-111-1-100002-2-220000i3−i3i3−i3−i3i3−i3i3-11-111-11-1i3−i3i3−i3−i3i3−i3i300000000000000000000
χ532222-2-2-2-2-22-2-22-2-122-2-222-1-1-1111111-1-111-1-111-1-10000-222-20000−i3i3−i3i3i3−i3i3−i31-11-1-11-11i3−i3i3−i3−i3i3−i3i300000000000000000000
χ542222-2-2-2-2-22-2-22-2-122-2-222-1-1-1111111-1-111-1-111-1-10000-222-20000i3−i3i3−i3−i3i3−i3i31-11-1-11-11−i3i3−i3i3i3−i3i3−i300000000000000000000
χ552222-2-2-2-2-2-22-2-2222222-2-2222-2-2-2-2-2-2-2-2222222-2-22-2-22000000002-2-22-222-2000000000000000000000000000000000000
χ562222-2-2-2-2-2-22-2-2222222-2-2222-2-2-2-2-2-2-2-2222222-2-2-222-200000000-222-22-2-22000000000000000000000000000000000000
χ572222-2-2-2-2-2-22-2-22-12222-2-2-1-1-111111111-1-1-1-1-1-1112-2-2200000000-111-11-1-11−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3i3−i3−i3i300000000000000000000
χ582222-2-2-2-2-2-22-2-22-12222-2-2-1-1-111111111-1-1-1-1-1-1112-2-2200000000-111-11-1-11i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3−i3i3i3−i300000000000000000000
χ592222-2-2-2-2-2-22-2-22-12222-2-2-1-1-111111111-1-1-1-1-1-111-222-2000000001-1-11-111-1−i3i3i3−i3i3−i3−i3i3i3−i3−i3i3−i3i3i3−i300000000000000000000
χ602222-2-2-2-2-2-22-2-22-12222-2-2-1-1-111111111-1-1-1-1-1-111-222-2000000001-1-11-111-1i3−i3−i3i3−i3i3i3−i3−i3i3i3−i3i3−i3−i3i300000000000000000000
χ612-2-2222-2-2222-2-2-222-22-22-22-2-222-2-22-22-22-22-22-22-200000000000000000000000000000000000022-2-222-2-2000000000000
χ622-2-2222-2-2222-2-2-222-22-22-22-2-222-2-22-22-22-22-22-22-2000000000000000000000000000000000000-2-222-2-222000000000000
χ632-2-2222-2-22-2-2-22222-2-22-222-2-222-2-22-2-22-222-2-22-2200000000000000000000000000000000000000000000000000002i−2i2i−2i
χ642-2-2222-2-22-2-2-22222-2-22-222-2-222-2-22-2-22-222-2-22-220000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ652-2-2222-2-2-22-22-222-222-2-222-2-222-2-2-222-2-22-222-2-220000000000000000000000000000000000000000000000002i−2i2i−2i0000
χ662-2-2222-2-2-22-22-222-222-2-222-2-222-2-2-222-2-22-222-2-22000000000000000000000000000000000000000000000000−2i2i−2i2i0000
χ672-2-2222-2-2-2-2222-22-22-222-22-2-222-2-2-22-222-2-22-222-2000000000000000000000000000000000000000000002i−2i2i−2i00000000
χ682-2-2222-2-2-2-2222-22-22-222-22-2-222-2-2-22-222-2-22-222-200000000000000000000000000000000000000000000−2i2i−2i2i00000000
χ692-2-22-2-222222-2-2-22-22-22-222-2-2-2-2222-22-22-2-22-22-2200000000000000000000000000000000000022-2-2-2-222000000000000
χ702-2-22-2-222222-2-2-22-22-22-222-2-2-2-2222-22-22-2-22-22-22000000000000000000000000000000000000-2-22222-2-2000000000000
χ712-2-22-2-2222-2-2-2222-222-22-22-2-2-2-2222-2-22-22-222-22-200000000000000000000000000000000000000000000000000002i−2i−2i2i
χ722-2-22-2-2222-2-2-2222-222-22-22-2-2-2-2222-2-22-22-222-22-20000000000000000000000000000000000000000000000000000−2i2i2i−2i
χ732-2-22-2-222-22-22-2222-2-222-22-2-2-2-222-222-2-222-2-222-20000000000000000000000000000000000000000000000002i−2i−2i2i0000
χ742-2-22-2-222-22-22-2222-2-222-22-2-2-2-222-222-2-222-2-222-2000000000000000000000000000000000000000000000000−2i2i2i−2i0000
χ752-2-22-2-222-2-2222-222-22-2-222-2-2-2-222-22-222-22-22-2-22000000000000000000000000000000000000000000002i−2i−2i2i00000000
χ762-2-22-2-222-2-2222-222-22-2-222-2-2-2-222-22-222-22-22-2-2200000000000000000000000000000000000000000000−2i2i2i−2i00000000
χ7744-4-44i−4i4i−4i0000004000000-44-44i−4i4i−4i0000000000000000000000000000000000000000000000002-22-22i−2i2i−2i000000000000
χ7844-4-44i−4i4i−4i0000004000000-44-44i−4i4i−4i000000000000000000000000000000000000000000000000-22-22−2i2i−2i2i000000000000
χ7944-4-4−4i4i−4i4i0000004000000-44-4−4i4i−4i4i0000000000000000000000000000000000000000000000002-22-2−2i2i−2i2i000000000000
χ8044-4-4−4i4i−4i4i0000004000000-44-4−4i4i−4i4i000000000000000000000000000000000000000000000000-22-222i−2i2i−2i000000000000
χ814-44-44i−4i−4i4i0000004000000-4-444i−4i−4i4i0000000000000000000000000000000000000000000000002-2-222i−2i−2i2i000000000000
χ824-44-44i−4i−4i4i0000004000000-4-444i−4i−4i4i000000000000000000000000000000000000000000000000-222-2−2i2i2i−2i000000000000
χ834-44-4−4i4i4i−4i0000004000000-4-44−4i4i4i−4i0000000000000000000000000000000000000000000000002-2-22−2i2i2i−2i000000000000
χ844-44-4−4i4i4i−4i0000004000000-4-44−4i4i4i−4i000000000000000000000000000000000000000000000000-222-22i−2i−2i2i000000000000
χ854-4-4444-4-4444-4-4-4-24-44-44-4-222-2-222-22-22-22-22-22-2200000000000000000000000000000000000000000000000000000000
χ864-4-4444-4-44-4-4-444-24-4-44-44-222-2-222-222-22-2-222-22-200000000000000000000000000000000000000000000000000000000
χ874-4-4444-4-4-44-44-44-2-444-4-44-222-2-2222-2-222-22-2-222-200000000000000000000000000000000000000000000000000000000
χ884-4-4444-4-4-4-4444-4-2-44-444-4-222-2-2222-22-2-222-22-2-2200000000000000000000000000000000000000000000000000000000
χ894-4-44-4-444444-4-4-4-2-44-44-44-22222-2-2-22-22-222-22-22-200000000000000000000000000000000000000000000000000000000
χ904-4-44-4-4444-4-4-444-2-444-44-4-22222-2-2-222-22-22-2-22-2200000000000000000000000000000000000000000000000000000000
χ914-4-44-4-444-44-44-44-24-4-444-4-22222-2-22-2-222-2-222-2-2200000000000000000000000000000000000000000000000000000000
χ924-4-44-4-444-4-4444-4-24-44-4-44-22222-2-22-22-2-22-22-222-200000000000000000000000000000000000000000000000000000000
χ9388-8-88i−8i8i−8i000000-40000004-44−4i4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ9488-8-8−8i8i−8i8i000000-40000004-444i−4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ958-88-88i−8i−8i8i000000-400000044-4−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8−8i8i8i−8i000000-400000044-44i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000

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