Finite Group Databasebeta

← Group #10823188

Character table — Group #10823188

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444448888888888888888888888888888888888881212121212121212242424242424242424242424
order1222222222223444444446666666666612121212121212122244444466668888121212121212121212121212242424242424242444444444222244448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
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
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-11111-1-1-1-111111111-1-1-1-1111-1-1-1-1111-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-11111-1-1-1-111111111-1-1-1-1111-1-1-1-1111-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111
χ1111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1111-1-1-1-1111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111
χ1211111111-1-1-1-11111-1-1-1-111111111-1-1-1-1111-1-1-1-1111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1
χ1311111111-1-1-1-11111-1-1-1-111111111-1-1-1-1111-1-1-1-11-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111
χ1411111111-1-1-1-11111-1-1-1-111111111-1-1-1-1111-1-1-1-11-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1
χ1511111111-1-1-1-11111-1-1-1-111111111-1-1-1-1111-1-1-1-11-1-111-1-111-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1
χ1611111111-1-1-1-11111-1-1-1-111111111-1-1-1-1111-1-1-1-11-1-111-1-111-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111
χ172222222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-200000000000000000000000000000000000022-2-222-2-2000000000000
χ182222222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2000000000000000000000000000000000000-2-222-2-222000000000000
χ19222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ20222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-2-2-2-2-1-1-1-1111111111111111100000000000000000000
χ21222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222221111-2-2-2-21111-1-1-1-1-1-1-1-11111111100000000000000000000
χ22222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211112222111111111111-1-1-1-1-1-1-1-100000000000000000000
χ2322222222-2-2-2-22-2-2-22222-22222222-2-2-2-2-2-2-22222-200000000000000000000000000000000000022-2-2-2-222000000000000
χ2422222222-2-2-2-22-2-2-22222-22222222-2-2-2-2-2-2-22222-2000000000000000000000000000000000000-2-22222-2-2000000000000
χ2522222222-2-2-2-2-1222-2-2-2-22-1-1-1-1-1-1-11111-1-1-11111-122-2-222-2-2-1-1-1-122-2-21111-1-1-1-11111-1-1-1-1111100000000000000000000
χ2622222222-2-2-2-2-1222-2-2-2-22-1-1-1-1-1-1-11111-1-1-11111-122-2-2-2-222-1-1-1-1-2-22211111111-1-1-1-11111-1-1-1-100000000000000000000
χ2722222222-2-2-2-2-1222-2-2-2-22-1-1-1-1-1-1-11111-1-1-11111-1-2-22222-2-21111-2-222-1-1-1-1-1-1-1-111111111-1-1-1-100000000000000000000
χ2822222222-2-2-2-2-1222-2-2-2-22-1-1-1-1-1-1-11111-1-1-11111-1-2-222-2-222111122-2-2-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000
χ292222-2-2-2-222-2-2222-222-2-2-22-2-2-2-22222-2-222-222-2-2-20000000000000000000000000000000000000000000000002i−2i2i−2i0000
χ302222-2-2-2-222-2-2222-222-2-2-22-2-2-2-22222-2-222-222-2-2-2000000000000000000000000000000000000000000000000−2i2i−2i2i0000
χ312222-2-2-2-222-2-22-2-22-2-22222-2-2-2-22222-2-2-2-22-2-22222-22-2000022-2-2000022-2-2000000000000000000000000000000000000
χ322222-2-2-2-222-2-22-2-22-2-22222-2-2-2-22222-2-2-2-22-2-2222-22-220000-2-2220000-2-222000000000000000000000000000000000000
χ332222-2-2-2-222-2-2-1-2-22-2-2222-11111-1-1-1-11111-111-1-1-12-22-20000-1-1110000-1-111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i300000000000000000000
χ342222-2-2-2-222-2-2-1-2-22-2-2222-11111-1-1-1-11111-111-1-1-12-22-20000-1-1110000-1-111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i300000000000000000000
χ352222-2-2-2-222-2-2-1-2-22-2-2222-11111-1-1-1-11111-111-1-1-1-22-22000011-1-1000011-1-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i300000000000000000000
χ362222-2-2-2-222-2-2-1-2-22-2-2222-11111-1-1-1-11111-111-1-1-1-22-22000011-1-1000011-1-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i300000000000000000000
χ372222-2-2-2-2-2-222222-2-2-222-22-2-2-2-222-2-22222-2-2-222-20000000000000000000000000000000000000000000000002i−2i−2i2i0000
χ382222-2-2-2-2-2-222222-2-2-222-22-2-2-2-222-2-22222-2-2-222-2000000000000000000000000000000000000000000000000−2i2i2i−2i0000
χ392222-2-2-2-2-2-2222-2-2222-2-222-2-2-2-222-2-222-2-2222-2-222-2-22000022-2-20000-2-222000000000000000000000000000000000000
χ402222-2-2-2-2-2-2222-2-2222-2-222-2-2-2-222-2-222-2-2222-2-22-222-20000-2-222000022-2-2000000000000000000000000000000000000
χ412222-2-2-2-2-2-222-1-2-2222-2-22-11111-1-111-1-111-1-1-111-12-2-220000-1-111000011-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i300000000000000000000
χ422222-2-2-2-2-2-222-1-2-2222-2-22-11111-1-111-1-111-1-1-111-12-2-220000-1-111000011-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i300000000000000000000
χ432222-2-2-2-2-2-222-1-2-2222-2-22-11111-1-111-1-111-1-1-111-1-222-2000011-1-10000-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i300000000000000000000
χ442222-2-2-2-2-2-222-1-2-2222-2-22-11111-1-111-1-111-1-1-111-1-222-2000011-1-10000-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i300000000000000000000
χ452-22-222-2-22-22-222-222-22-2-2-222-2-22-22-22-22-222-22-2-20000000000002i−2i2i−2i0000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ462-22-222-2-22-22-222-222-22-2-2-222-2-22-22-22-22-222-22-2-2000000000000−2i2i−2i2i000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ472-22-222-2-22-22-22-22-2-22-222-222-2-22-22-22-2-22-2-22-22200000000000000000000000000000000000000000000000000002-22-2
χ482-22-222-2-22-22-22-22-2-22-222-222-2-22-22-22-2-22-2-22-2220000000000000000000000000000000000000000000000000000-22-22
χ492-22-222-2-22-22-2-12-222-22-2-21-1-111-11-11-11-11-1-11-11100000000−i3i3−i3i32i−2i2i−2i−i3i3−i3i33−33−33−33−3−ii−ii−ii−ii00000000000000000000
χ502-22-222-2-22-22-2-12-222-22-2-21-1-111-11-11-11-11-1-11-11100000000−i3i3−i3i3−2i2i−2i2i−i3i3−i3i3−33−33−33−33i−ii−ii−ii−i00000000000000000000
χ512-22-222-2-22-22-2-12-222-22-2-21-1-111-11-11-11-11-1-11-11100000000i3−i3i3−i32i−2i2i−2ii3−i3i3−i3−33−33−33−33−ii−ii−ii−ii00000000000000000000
χ522-22-222-2-22-22-2-12-222-22-2-21-1-111-11-11-11-11-1-11-11100000000i3−i3i3−i3−2i2i−2i2ii3−i3i3−i33−33−33−33−3i−ii−ii−ii−i00000000000000000000
χ532-22-222-2-2-22-2222-22-22-22-2-222-2-22-2-22-222-22-22-22-20000000000002i−2i−2i2i0000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ542-22-222-2-2-22-2222-22-22-22-2-222-2-22-2-22-222-22-22-22-2000000000000−2i2i2i−2i000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ552-22-222-2-2-22-222-22-22-22-22-222-2-22-2-22-22-22-22-22-2200000000000000000000000000000000000000000000000000002-2-22
χ562-22-222-2-2-22-222-22-22-22-22-222-2-22-2-22-22-22-22-22-220000000000000000000000000000000000000000000000000000-222-2
χ572-22-222-2-2-22-22-12-22-22-22-21-1-111-111-11-1-11-11-11-1100000000−i3i3−i3i32i−2i−2i2ii3−i3i3−i33−33−3−33−33−ii−iii−ii−i00000000000000000000
χ582-22-222-2-2-22-22-12-22-22-22-21-1-111-111-11-1-11-11-11-1100000000−i3i3−i3i3−2i2i2i−2ii3−i3i3−i3−33−333−33−3i−ii−i−ii−ii00000000000000000000
χ592-22-222-2-2-22-22-12-22-22-22-21-1-111-111-11-1-11-11-11-1100000000i3−i3i3−i32i−2i−2i2i−i3i3−i3i3−33−333−33−3−ii−iii−ii−i00000000000000000000
χ602-22-222-2-2-22-22-12-22-22-22-21-1-111-111-11-1-11-11-11-1100000000i3−i3i3−i3−2i2i2i−2i−i3i3−i3i33−33−3−33−33i−ii−i−ii−ii00000000000000000000
χ612-22-2-2-2222-2-2222-2-22-2-222-2-2-2222-22-2-222-2-22-2-222000000000000000000000000000000000000000000002-22-200000000
χ622-22-2-2-2222-2-2222-2-22-2-222-2-2-2222-22-2-222-2-22-2-22200000000000000000000000000000000000000000000-22-2200000000
χ632-22-2-2-2222-2-222-222-222-2-2-2-2-2222-22-2-22-222-222-2-200002i−2i2i−2i0000000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ642-22-2-2-2222-2-222-222-222-2-2-2-2-2222-22-2-22-222-222-2-20000−2i2i−2i2i000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ652-22-2-2-2222-2-22-1-222-222-2-2111-1-1-11-111-11-1-11-1-11100002i−2i2i−2i−i3i3i3−i30000−i3i3i3−i3−iii−i−iii−i3−3−333−3−3300000000000000000000
χ662-22-2-2-2222-2-22-1-222-222-2-2111-1-1-11-111-11-1-11-1-11100002i−2i2i−2ii3−i3−i3i30000i3−i3−i3i3−iii−i−iii−i−333−3−333−300000000000000000000
χ672-22-2-2-2222-2-22-1-222-222-2-2111-1-1-11-111-11-1-11-1-1110000−2i2i−2i2i−i3i3i3−i30000−i3i3i3−i3i−i−iii−i−ii−333−3−333−300000000000000000000
χ682-22-2-2-2222-2-22-1-222-222-2-2111-1-1-11-111-11-1-11-1-1110000−2i2i−2i2ii3−i3−i3i30000i3−i3−i3i3i−i−iii−i−ii3−3−333−3−3300000000000000000000
χ692-22-2-2-222-222-222-2-2-222-22-2-2-2222-2-222-22-2-2-222-22000000000000000000000000000000000000000000002-2-2200000000
χ702-22-2-2-222-222-222-2-2-222-22-2-2-2222-2-222-22-2-2-222-2200000000000000000000000000000000000000000000-222-200000000
χ712-22-2-2-222-222-22-2222-2-22-2-2-2-2222-2-222-2-2222-2-22-200002i−2i−2i2i0000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ722-22-2-2-222-222-22-2222-2-22-2-2-2-2222-2-222-2-2222-2-22-20000−2i2i2i−2i000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ732-22-2-2-222-222-2-1-2222-2-22-2111-1-1-111-1-111-1-1-111-1100002i−2i−2i2i−i3i3i3−i30000i3−i3−i3i3−iii−ii−i−ii3−3−33−333−300000000000000000000
χ742-22-2-2-222-222-2-1-2222-2-22-2111-1-1-111-1-111-1-1-111-1100002i−2i−2i2ii3−i3−i3i30000−i3i3i3−i3−iii−ii−i−ii−333−33−3−3300000000000000000000
χ752-22-2-2-222-222-2-1-2222-2-22-2111-1-1-111-1-111-1-1-111-110000−2i2i2i−2i−i3i3i3−i30000i3−i3−i3i3i−i−ii−iii−i−333−33−3−3300000000000000000000
χ762-22-2-2-222-222-2-1-2222-2-22-2111-1-1-111-1-111-1-1-111-110000−2i2i2i−2ii3−i3−i3i30000−i3i3i3−i3i−i−ii−iii−i3−3−33−333−300000000000000000000
χ77444444444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000000000000000000000000000
χ7844444444-4-4-4-4-2-4-4-44444-4-2-2-2-2-2-2-22222222-2-2-2-2200000000000000000000000000000000000000000000000000000000
χ794444-4-4-4-444-4-4-244-444-4-4-4-22222-2-2-2-222-2-22-2-222200000000000000000000000000000000000000000000000000000000
χ804444-4-4-4-4-4-444-244-4-4-444-4-22222-2-222-2-2-2-2222-2-2200000000000000000000000000000000000000000000000000000000
χ8144-4-44-44-4000040000000044-44-4-4-40000000000000000000000000000000000000000000000000000004i−4i000000000000
χ8244-4-44-44-4000040000000044-44-4-4-4000000000000000000000000000000000000000000000000000000−4i4i000000000000
χ8344-4-4-44-4400004000000004-44-44-4-40000000000000000000000000000000000000000000000004i−4i000000000000000000
χ8444-4-4-44-4400004000000004-44-44-4-4000000000000000000000000000000000000000000000000−4i4i000000000000000000
χ854-44-444-4-44-44-4-2-44-4-44-4442-2-222-22-22-222-222-22-2-200000000000000000000000000000000000000000000000000000000
χ864-44-444-4-4-44-44-2-44-44-44-442-2-222-222-22-22-22-22-22-200000000000000000000000000000000000000000000000000000000
χ874-44-4-4-4444-4-44-24-4-44-4-444222-2-2-22-222-2-222-222-2-200000000000000000000000000000000000000000000000000000000
χ884-44-4-4-444-444-4-24-4-4-444-44222-2-2-222-2-22-2222-2-22-200000000000000000000000000000000000000000000000000000000
χ894-4-444-4-440000400000000-44-4-44-4400000000000000000000000000000000000000000000000000004-400000000000000
χ904-4-444-4-440000400000000-44-4-44-440000000000000000000000000000000000000000000000000000-4400000000000000
χ914-4-44-444-40000400000000-4-444-4-44000000000000000000000000000000000000000000000000004-40000000000000000
χ924-4-44-444-40000400000000-4-444-4-4400000000000000000000000000000000000000000000000000-440000000000000000
χ9388-8-88-88-80000-400000000-4-44-444400000000000000000000000000000000000000000000000000000000000000000000
χ9488-8-8-88-880000-400000000-44-44-44400000000000000000000000000000000000000000000000000000000000000000000
χ958-8-888-8-880000-4000000004-444-44-400000000000000000000000000000000000000000000000000000000000000000000
χ968-8-88-888-80000-40000000044-4-444-400000000000000000000000000000000000000000000000000000000000000000000

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