Finite Group Databasebeta

← Group #10702266

Character table — Group #10702266

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444448888888888888888888888888888888888881212121212121212242424242424242424242424
order122222222222222222223666666666666666666644444444444412121212121212121212121212121212121212121212121222222222444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ911-1-111-1-111111-1-1-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−i11-1-1
χ1011-1-111-1-111111-1-1-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111−i−iii−i−iii-1-111
χ1111-1-111-1-111111-1-1-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii11-1-1
χ1211-1-111-1-111111-1-1-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111ii−i−iii−i−i-1-111
χ1311-1-111-1-111111-1-1-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-111ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1ii−i−i−i−iii-1-111
χ1411-1-111-1-111111-1-1-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-111ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111−i−iiiii−i−i11-1-1
χ1511-1-111-1-111111-1-1-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-111−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1−i−iiiii−i−i-1-111
χ1611-1-111-1-111111-1-1-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-111−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111ii−i−i−i−iii11-1-1
χ1722222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ1822222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000000000000000
χ1922222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-11111111100000000000000000000
χ2022222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-100000000000000000000
χ212222222222-2-2-22-2-2-22-2-22222222222-2-2-2-22-2-2-22-2000000000000000000000000000000000000000000002-22-200000000
χ222222222222-2-2-22-2-2-22-2-22222222222-2-2-2-22-2-2-22-200000000000000000000000000000000000000000000-22-2200000000
χ2322222222-2-222-2-22-2-2-22-222222222-2-222-2-2-22-2-2-220000000000000000000000000000000000000000000000002-22-20000
χ2422222222-2-222-2-22-2-2-22-222222222-2-222-2-2-22-2-2-22000000000000000000000000000000000000000000000000-22-220000
χ2522222222-2-2-2-22-2-222-2-2222222222-2-2-2-222-2-222-2-22-22-20000000022-2-222-2-2000000000000000000000000000000000000
χ2622222222-2-2-2-22-2-222-2-2222222222-2-2-2-222-2-222-2-2-22-2200000000-2-222-2-222000000000000000000000000000000000000
χ2722222222-2-2-2-22-2-222-2-22-1-1-1-1-1-1-1-11111-1-111-1-1112-22-200000000-1-111-1-11133−3−333−3−333−3−333−3−300000000000000000000
χ2822222222-2-2-2-22-2-222-2-22-1-1-1-1-1-1-1-11111-1-111-1-1112-22-200000000-1-111-1-111−3−333−3−333−3−333−3−33300000000000000000000
χ2922222222-2-2-2-22-2-222-2-22-1-1-1-1-1-1-1-11111-1-111-1-111-22-220000000011-1-111-1-133−3−333−3−3−3−333−3−33300000000000000000000
χ3022222222-2-2-2-22-2-222-2-22-1-1-1-1-1-1-1-11111-1-111-1-111-22-220000000011-1-111-1-1−3−333−3−33333−3−333−3−300000000000000000000
χ312222-2-2-2-22-22-22222-2-2-2-22222-2-2-2-22-22-22-2222-2-2-200000000000000000000000000000000000022-2-222-2-2000000000000
χ322222-2-2-2-22-22-22222-2-2-2-22222-2-2-2-22-22-22-2222-2-2-2000000000000000000000000000000000000-2-222-2-222000000000000
χ332222-2-2-2-22-2-22-22-2-22-2222222-2-2-2-22-2-22-222-2-22-2200002i−2i2i−2i0000000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ342222-2-2-2-22-2-22-22-2-22-2222222-2-2-2-22-2-22-222-2-22-220000−2i2i−2i2i000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ352222-2-2-2-22-2-22-22-2-22-222-1-1-1-11111-111-11-1-111-11-100002i−2i2i−2i00003−33−33−33−3−ii−ii−ii−ii−i3i3−i3i3−i3i3−i3i300000000000000000000
χ362222-2-2-2-22-2-22-22-2-22-222-1-1-1-11111-111-11-1-111-11-100002i−2i2i−2i0000−33−33−33−33−ii−ii−ii−iii3−i3i3−i3i3−i3i3−i300000000000000000000
χ372222-2-2-2-22-2-22-22-2-22-222-1-1-1-11111-111-11-1-111-11-10000−2i2i−2i2i00003−33−33−33−3i−ii−ii−ii−ii3−i3i3−i3i3−i3i3−i300000000000000000000
χ382222-2-2-2-22-2-22-22-2-22-222-1-1-1-11111-111-11-1-111-11-10000−2i2i−2i2i0000−33−33−33−33i−ii−ii−ii−i−i3i3−i3i3−i3i3−i3i300000000000000000000
χ392222-2-2-2-2-222-2-2-22-222-222222-2-2-2-2-222-2-22-22-222-2000000002i−2i2i−2i00000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ402222-2-2-2-2-222-2-2-22-222-222222-2-2-2-2-222-2-22-22-222-200000000−2i2i−2i2i0000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ412222-2-2-2-2-222-2-2-22-222-22-1-1-1-111111-1-111-11-11-1-11000000002i−2i2i−2i3−3−333−3−33i3−i3−i3i3i3−i3−i3i3−iii−i−iii−i00000000000000000000
χ422222-2-2-2-2-222-2-2-22-222-22-1-1-1-111111-1-111-11-11-1-11000000002i−2i2i−2i−333−3−333−3−i3i3i3−i3−i3i3i3−i3−iii−i−iii−i00000000000000000000
χ432222-2-2-2-2-222-2-2-22-222-22-1-1-1-111111-1-111-11-11-1-1100000000−2i2i−2i2i3−3−333−3−33−i3i3i3−i3−i3i3i3−i3i−i−iii−i−ii00000000000000000000
χ442222-2-2-2-2-222-2-2-22-222-22-1-1-1-111111-1-111-11-11-1-1100000000−2i2i−2i2i−333−3−333−3i3−i3−i3i3i3−i3−i3i3i−i−iii−i−ii00000000000000000000
χ452222-2-2-2-2-22-222-2-22-222-22222-2-2-2-2-22-222-2-2-22-22200000000000000000000000000000000000000000000000000002i−2i2i−2i
χ462222-2-2-2-2-22-222-2-22-222-22222-2-2-2-2-22-222-2-2-22-2220000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ4722-2-222-2-222222-2-2-2-2-2-22-1-11111-1-1-1-1-1-1-1-111111122-2-22i2i−2i−2i2i2i−2i−2i-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii00000000000000000000
χ4822-2-222-2-222222-2-2-2-2-2-22-1-11111-1-1-1-1-1-1-1-111111122-2-2−2i−2i2i2i−2i−2i2i2i-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i00000000000000000000
χ4922-2-222-2-222222-2-2-2-2-2-22-1-11111-1-1-1-1-1-1-1-1111111-2-2222i2i−2i−2i−2i−2i2i2i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000000000000000
χ5022-2-222-2-222222-2-2-2-2-2-22-1-11111-1-1-1-1-1-1-1-1111111-2-222−2i−2i2i2i2i2i−2i−2i1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii00000000000000000000
χ5122-2-222-2-222-2-2-2-2222-22-222-2-2-2-22222-2-2-2-2-2222-22000000000000000000000000000000000000000000002i−2i−2i2i00000000
χ5222-2-222-2-222-2-2-2-2222-22-222-2-2-2-22222-2-2-2-2-2222-2200000000000000000000000000000000000000000000−2i2i2i−2i00000000
χ5322-2-222-2-2-2-222-22-2222-2-222-2-2-2-222-2-222-2-22-2222-20000000000000000000000000000000000000000000000002i−2i−2i2i0000
χ5422-2-222-2-2-2-222-22-2222-2-222-2-2-2-222-2-222-2-22-2222-2000000000000000000000000000000000000000000000000−2i2i2i−2i0000
χ5522-2-222-2-2-2-2-2-2222-2-222222-2-2-2-222-2-2-2-22222-2-2222-2-220000000022-2-2-2-222000000000000000000000000000000000000
χ5622-2-222-2-2-2-2-2-2222-2-222222-2-2-2-222-2-2-2-22222-2-222-222-200000000-2-22222-2-2000000000000000000000000000000000000
χ5722-2-222-2-2-2-2-2-2222-2-2222-1-11111-1-11111-1-1-1-111-1-12-2-2200000000-1-11111-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i300000000000000000000
χ5822-2-222-2-2-2-2-2-2222-2-2222-1-11111-1-11111-1-1-1-111-1-12-2-2200000000-1-11111-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i300000000000000000000
χ5922-2-222-2-2-2-2-2-2222-2-2222-1-11111-1-11111-1-1-1-111-1-1-222-20000000011-1-1-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i300000000000000000000
χ6022-2-222-2-2-2-2-2-2222-2-2222-1-11111-1-11111-1-1-1-111-1-1-222-20000000011-1-1-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i300000000000000000000
χ6122-2-2-2-2222-22-22-2-2-2222-222-2-222-2-22-22-22-2-2-2-222200000000000000000000000000000000000022-2-2-2-222000000000000
χ6222-2-2-2-2222-22-22-2-2-2222-222-2-222-2-22-22-22-2-2-2-2222000000000000000000000000000000000000-2-22222-2-2000000000000
χ6322-2-2-2-2222-2-22-2-222-22-2222-2-222-2-22-2-22-22-222-22-200002-2-220000000000002-22-2-22-220000000000000000000000000000
χ6422-2-2-2-2222-2-22-2-222-22-2222-2-222-2-22-2-22-22-222-22-20000-222-2000000000000-22-222-22-20000000000000000000000000000
χ6522-2-2-2-2222-2-22-2-222-22-22-1-111-1-111-111-11-11-1-11-1100002-2-2200003−33−3−33−33-11-111-11-1−33−333−33−300000000000000000000
χ6622-2-2-2-2222-2-22-2-222-22-22-1-111-1-111-111-11-11-1-11-1100002-2-220000−33−333−33−3-11-111-11-13−33−3−33−3300000000000000000000
χ6722-2-2-2-2222-2-22-2-222-22-22-1-111-1-111-111-11-11-1-11-110000-222-200003−33−3−33−331-11-1-11-113−33−3−33−3300000000000000000000
χ6822-2-2-2-2222-2-22-2-222-22-22-1-111-1-111-111-11-11-1-11-110000-222-20000−33−333−33−31-11-1-11-11−33−333−33−300000000000000000000
χ6922-2-2-2-222-222-2-22-22-2-22222-2-222-2-2-222-2-222-22-2-22000000002-2-2200000000000000002-2-22-222-200000000000000000000
χ7022-2-2-2-222-222-2-22-22-2-22222-2-222-2-2-222-2-222-22-2-2200000000-222-20000000000000000-222-22-2-2200000000000000000000
χ7122-2-2-2-222-222-2-22-22-2-222-1-111-1-1111-1-111-1-11-111-1000000002-2-223−3−33−333−33−3−33−333−3-111-11-1-1100000000000000000000
χ7222-2-2-2-222-222-2-22-22-2-222-1-111-1-1111-1-111-1-11-111-1000000002-2-22−333−33−3−33−333−33−3−33-111-11-1-1100000000000000000000
χ7322-2-2-2-222-222-2-22-22-2-222-1-111-1-1111-1-111-1-11-111-100000000-222-23−3−33−333−3−333−33−3−331-1-11-111-100000000000000000000
χ7422-2-2-2-222-222-2-22-22-2-222-1-111-1-1111-1-111-1-11-111-100000000-222-2−333−33−3−333−3−33−333−31-1-11-111-100000000000000000000
χ7522-2-2-2-222-22-22222-22-2-2-222-2-222-2-2-22-222-222-22-2-200000000000000000000000000000000000000000000000000002i−2i−2i2i
χ7622-2-2-2-222-22-22222-22-2-2-222-2-222-2-2-22-222-222-22-2-20000000000000000000000000000000000000000000000000000−2i2i2i−2i
χ774444444444-4-4-44-4-4-44-4-4-2-2-2-2-2-2-2-2-2-22222-2222-2200000000000000000000000000000000000000000000000000000000
χ7844444444-4-444-4-44-4-4-44-4-2-2-2-2-2-2-2-222-2-2222-2222-200000000000000000000000000000000000000000000000000000000
χ794444-4-4-4-44-44-44444-4-4-4-4-2-2-2-22222-22-22-22-2-2-222200000000000000000000000000000000000000000000000000000000
χ804444-4-4-4-4-44-444-4-44-444-4-2-2-2-222222-22-2-2222-22-2-200000000000000000000000000000000000000000000000000000000
χ8144-4-444-4-444-4-4-4-4444-44-4-2-22222-2-2-2-222222-2-2-22-200000000000000000000000000000000000000000000000000000000
χ8244-4-444-4-4-4-444-44-4444-4-4-2-22222-2-222-2-222-22-2-2-2200000000000000000000000000000000000000000000000000000000
χ8344-4-4-4-4444-44-44-4-4-4444-4-2-222-2-222-22-22-22222-2-2-200000000000000000000000000000000000000000000000000000000
χ8444-4-4-4-444-44-44444-44-4-4-4-2-222-2-2222-22-2-22-2-22-22200000000000000000000000000000000000000000000000000000000
χ854-44-44-44-40000000000004-44-44-44-40000000000000000000000000000000000000000000000002-22-22-22-2000000000000
χ864-44-44-44-40000000000004-44-44-44-4000000000000000000000000000000000000000000000000-22-22-22-22000000000000
χ874-44-4-44-440000000000004-44-4-44-440000000000000000000000000000000000000000000000002-2-222-2-22000000000000
χ884-44-4-44-440000000000004-44-4-44-44000000000000000000000000000000000000000000000000-222-2-222-2000000000000
χ894-4-444-4-440000000000004-4-44-444-40000000000000000000000000000000000000000000000002-22-2-22-22000000000000
χ904-4-444-4-440000000000004-4-44-444-4000000000000000000000000000000000000000000000000-22-222-22-2000000000000
χ914-4-44-444-40000000000004-4-444-4-440000000000000000000000000000000000000000000000002-2-22-222-2000000000000
χ924-4-44-444-40000000000004-4-444-4-44000000000000000000000000000000000000000000000000-222-22-2-22000000000000
χ938-88-88-88-8000000000000-44-44-44-4400000000000000000000000000000000000000000000000000000000000000000000
χ948-88-8-88-88000000000000-44-444-44-400000000000000000000000000000000000000000000000000000000000000000000
χ958-8-888-8-88000000000000-444-44-4-4400000000000000000000000000000000000000000000000000000000000000000000
χ968-8-88-888-8000000000000-444-4-444-400000000000000000000000000000000000000000000000000000000000000000000

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