Finite Group Databasebeta

← Group #10702684

Character table — Group #10702684

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444448888888888888888888888888888888888881212121212121212242424242424242424242424
order1222444422222234444446661212121266666612121212121288888888888824242424242424242424242424242424242424242424242488888888224488888888
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
χ51111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ61111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
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
χ91111-1-1-1-111-1-1-1-1111-111-1111-1-1-1-111-1-1-1-1111-1-11ii−i−iii−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i11-1-1
χ101111-1-1-1-111-1-1-1-1111-111-1111-1-1-1-111-1-1-1-1111-1-11ii−i−iii−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii-1-111−i−iii-1-111
χ111111-1-1-1-111-1-1-1-1111-111-1111-1-1-1-111-1-1-1-1111-1-11ii−i−i−i−iii-1-111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i11-1-1−i−iii-1-111
χ121111-1-1-1-111-1-1-1-1111-111-1111-1-1-1-111-1-1-1-1111-1-11ii−i−i−i−iii-1-111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii-1-111ii−i−i11-1-1
χ131111-1-1-1-111-1-1-1-1111-111-1111-1-1-1-111-1-1-1-1111-1-11−i−iiiii−i−i-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i-1-111−i−iii11-1-1
χ141111-1-1-1-111-1-1-1-1111-111-1111-1-1-1-111-1-1-1-1111-1-11−i−iiiii−i−i-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii11-1-1ii−i−i-1-111
χ151111-1-1-1-111-1-1-1-1111-111-1111-1-1-1-111-1-1-1-1111-1-11−i−iii−i−iii11-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i-1-111ii−i−i-1-111
χ161111-1-1-1-111-1-1-1-1111-111-1111-1-1-1-111-1-1-1-1111-1-11−i−iii−i−iii11-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii11-1-1
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
χ212222222222-2-2-2-22-2-22-2-22222222222-2-2-2-2-2-2-222-2000000000000000000000000000000000000000000002-22-200000000
χ222222222222-2-2-2-22-2-22-2-22222222222-2-2-2-2-2-2-222-200000000000000000000000000000000000000000000-22-2200000000
χ2322222222-2-222-2-222-2-22-2-22222222-2-222-2-22-2-2-2-2200002-22-200000000000022-2-222-2-20000000000000000000000000000
χ2422222222-2-222-2-222-2-22-2-22222222-2-222-2-22-2-2-2-220000-22-22000000000000-2-222-2-2220000000000000000000000000000
χ2522222222-2-222-2-2-12-2-22-2-2-1-1-1-1-1-1-111-1-111-11111-100002-22-20000−i3−i3i3i3−i3−i3i3i3-1-111-1-111−i3−i3i3i3−i3−i3i3i300000000000000000000
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χ2722222222-2-222-2-2-12-2-22-2-2-1-1-1-1-1-1-111-1-111-11111-10000-22-220000−i3−i3i3i3−i3−i3i3i311-1-111-1-1i3i3−i3−i3i3i3−i3−i300000000000000000000
χ2822222222-2-222-2-2-12-2-22-2-2-1-1-1-1-1-1-111-1-111-11111-10000-22-220000i3i3−i3−i3i3i3−i3−i311-1-111-1-1−i3−i3i3i3−i3−i3i3i300000000000000000000
χ2922222222-2-2-2-2222-22-2-22-22222222-2-2-2-222-222-2-2-20000000000000000000000000000000000000000000000002-22-20000
χ3022222222-2-2-2-2222-22-2-22-22222222-2-2-2-222-222-2-2-2000000000000000000000000000000000000000000000000-22-220000
χ312222-2-2-2-22222222-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-2000000000000000000000000000000000000000000002-2-2200000000
χ322222-2-2-2-22222222-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-200000000000000000000000000000000000000000000-222-200000000
χ332222-2-2-2-222-2-2-2-2-122-222-2-1-1-11111-1-11111-1-1-111-12i2i−2i−2i2i2i−2i−2i22-2-2−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1111100000000000000000000
χ342222-2-2-2-222-2-2-2-2-122-222-2-1-1-11111-1-11111-1-1-111-12i2i−2i−2i−2i−2i2i2i-2-222−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-100000000000000000000
χ352222-2-2-2-222-2-2-2-2-122-222-2-1-1-11111-1-11111-1-1-111-1−2i−2i2i2i2i2i−2i−2i-2-222iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-100000000000000000000
χ362222-2-2-2-222-2-2-2-2-122-222-2-1-1-11111-1-11111-1-1-111-1−2i−2i2i2i−2i−2i2i2i22-2-2iiii−i−i−i−iiiii−i−i−i−i-1-1-1-1111100000000000000000000
χ372222-2-2-2-2-2-222-2-22-222-222222-2-2-2-2-2-222-2-2-22222-20000000000000000000000000000000000000000000000002i−2i−2i2i0000
χ382222-2-2-2-2-2-222-2-22-222-222222-2-2-2-2-2-222-2-2-22222-2000000000000000000000000000000000000000000000000−2i2i2i−2i0000
χ392222-2-2-2-2-2-2-2-22222-222-22222-2-2-2-2-2-2-2-2222-2-222200002i−2i−2i2i0000000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ402222-2-2-2-2-2-2-2-22222-222-22222-2-2-2-2-2-2-2-2222-2-22220000−2i2i2i−2i000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ412222-2-2-2-2-2-2-2-222-12-222-22-1-1-111111111-1-1-111-1-1-100002i−2i−2i2i000033−3−3−3−333−i−iiiii−i−i−i3−i3i3i3i3i3−i3−i300000000000000000000
χ422222-2-2-2-2-2-2-2-222-12-222-22-1-1-111111111-1-1-111-1-1-100002i−2i−2i2i0000−3−33333−3−3−i−iiiii−i−ii3i3−i3−i3−i3−i3i3i300000000000000000000
χ432222-2-2-2-2-2-2-2-222-12-222-22-1-1-111111111-1-1-111-1-1-10000−2i2i2i−2i000033−3−3−3−333ii−i−i−i−iiii3i3−i3−i3−i3−i3i3i300000000000000000000
χ442222-2-2-2-2-2-2-2-222-12-222-22-1-1-111111111-1-1-111-1-1-10000−2i2i2i−2i0000−3−33333−3−3ii−i−i−i−iii−i3−i3i3i3i3i3−i3−i300000000000000000000
χ452-2-2222-2-22-22-22-22222-2-2-2-2-22-2-2222-22-22-222-22-2-200000000000000000000000000000000000000000000000000002i−2i2i−2i
χ462-2-2222-2-22-22-22-22222-2-2-2-2-22-2-2222-22-22-222-22-2-20000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ472-2-2222-2-22-2-22-222-2-2222-2-2-22-2-2222-2-22-22-2-222-22000000002-22-200000000000000002-22-22-22-200000000000000000000
χ482-2-2222-2-22-2-22-222-2-2222-2-2-22-2-2222-2-22-22-2-222-2200000000-22-220000000000000000-22-22-22-2200000000000000000000
χ492-2-2222-2-22-2-22-22-1-2-2222-211-111-1-1-111-11-111-1-11-1000000002-22-2−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3-11-11-11-1100000000000000000000
χ502-2-2222-2-22-2-22-22-1-2-2222-211-111-1-1-111-11-111-1-11-1000000002-22-2i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3-11-11-11-1100000000000000000000
χ512-2-2222-2-22-2-22-22-1-2-2222-211-111-1-1-111-11-111-1-11-100000000-22-22−i3i3−i3i3−i3i3−i3i3i3−i3i3−i3i3−i3i3−i31-11-11-11-100000000000000000000
χ522-2-2222-2-22-2-22-22-1-2-2222-211-111-1-1-111-11-111-1-11-100000000-22-22i3−i3i3−i3i3−i3i3−i3−i3i3−i3i3−i3i3−i3i31-11-11-11-100000000000000000000
χ532-2-2222-2-2-222-2-2222-2-2-222-2-22-2-222-222-2-222-22-22-200000000000000000000000000000000000022-2-222-2-2000000000000
χ542-2-2222-2-2-222-2-2222-2-2-222-2-22-2-222-222-2-222-22-22-2000000000000000000000000000000000000-2-222-2-222000000000000
χ552-2-2222-2-2-22-222-22-22-22-22-2-22-2-222-22-222-2-22-2-2222-22-2000000002-2-222-2-22000000000000000000000000000000000000
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χ572-2-2222-2-2-22-222-2-1-22-22-2211-111-1-11-11-1-111-111-1-12-22-200000000-111-1-111-1−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i300000000000000000000
χ582-2-2222-2-2-22-222-2-1-22-22-2211-111-1-11-11-1-111-111-1-12-22-200000000-111-1-111-1i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i300000000000000000000
χ592-2-2222-2-2-22-222-2-1-22-22-2211-111-1-11-11-1-111-111-1-1-22-22000000001-1-111-1-11−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3i3−i3−i3i300000000000000000000
χ602-2-2222-2-2-22-222-2-1-22-22-2211-111-1-11-11-1-111-111-1-1-22-22000000001-1-111-1-11i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3−i3i3i3−i300000000000000000000
χ612-2-22-2-2222-22-22-22-2-2-2222-2-2222-2-22-22-22-2-2-22-222000000002-2-2200000000000000002-22-2-22-2200000000000000000000
χ622-2-22-2-2222-22-22-22-2-2-2222-2-2222-2-22-22-22-2-2-22-22200000000-222-20000000000000000-22-222-22-200000000000000000000
χ632-2-22-2-2222-22-22-2-1-2-2-222211-1-1-111-11-11-1111-11-1-1000000002-2-223−33−3−33−333−33−3−33−33-11-111-11-100000000000000000000
χ642-2-22-2-2222-22-22-2-1-2-2-222211-1-1-111-11-11-1111-11-1-1000000002-2-22−33−333−33−3−33−333−33−3-11-111-11-100000000000000000000
χ652-2-22-2-2222-22-22-2-1-2-2-222211-1-1-111-11-11-1111-11-1-100000000-222-23−33−3−33−33−33−333−33−31-11-1-11-1100000000000000000000
χ662-2-22-2-2222-22-22-2-1-2-2-222211-1-1-111-11-11-1111-11-1-100000000-222-2−33−333−33−33−33−3−33−331-11-1-11-1100000000000000000000
χ672-2-22-2-2222-2-22-22222-2-2-22-2-2222-2-22-2-22-2222-2-22-200000000000000000000000000000000000000000000000000002i−2i−2i2i
χ682-2-22-2-2222-2-22-22222-2-2-22-2-2222-2-22-2-22-2222-2-22-20000000000000000000000000000000000000000000000000000−2i2i2i−2i
χ692-2-22-2-222-222-2-222-2222-2-2-2-2222-2-2-222-2-22-22-22-222i−2i−2i2i000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000000000000000
χ702-2-22-2-222-222-2-222-2222-2-2-2-2222-2-2-222-2-22-22-22-22−2i2i2i−2i00000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000000000
χ712-2-22-2-222-222-2-22-1-2222-2-211-1-1-1111-1-111-11-11-11-12i−2i−2i2i00000000−iii−ii−i−ii3−3−33−333−3−i3i3i3−i3i3−i3−i3i300000000000000000000
χ722-2-22-2-222-222-2-22-1-2222-2-211-1-1-1111-1-111-11-11-11-12i−2i−2i2i00000000−iii−ii−i−ii−333−33−3−33i3−i3−i3i3−i3i3i3−i300000000000000000000
χ732-2-22-2-222-222-2-22-1-2222-2-211-1-1-1111-1-111-11-11-11-1−2i2i2i−2i00000000i−i−ii−iii−i3−3−33−333−3i3−i3−i3i3−i3i3i3−i300000000000000000000
χ742-2-22-2-222-222-2-22-1-2222-2-211-1-1-1111-1-111-11-11-11-1−2i2i2i−2i00000000i−i−ii−iii−i−333−33−3−33−i3i3i3−i3i3−i3−i3i300000000000000000000
χ752-2-22-2-222-22-222-222-22-22-2-2-2222-2-2-22-222-22-222-2-20000000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ762-2-22-2-222-22-222-222-22-22-2-2-2222-2-2-22-222-22-222-2-2000000000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
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χ8244-4-44i−4i4i−4i00000040000004-4-44i−4i4i−4i000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13000000000000
χ8344-4-4−4i4i−4i4i00000040000004-4-4−4i4i−4i4i000000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23000000000000
χ8444-4-4−4i4i−4i4i00000040000004-4-4−4i4i−4i4i0000000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23000000000000
χ854-44-44i−4i−4i4i0000004000000-44-4−4i4i4i−4i0000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13000000000000
χ864-44-44i−4i−4i4i0000004000000-44-4−4i4i4i−4i000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13000000000000
χ874-44-4−4i4i4i−4i0000004000000-44-44i−4i−4i4i000000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23000000000000
χ884-44-4−4i4i4i−4i0000004000000-44-44i−4i−4i4i0000000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23000000000000
χ894-4-4444-4-44-44-44-4-2444-4-4-422-222-2-2-22-22-22-2-22-22200000000000000000000000000000000000000000000000000000000
χ904-4-4444-4-4-444-4-44-24-4-4-44422-222-2-22-2-222-2-22-22-2200000000000000000000000000000000000000000000000000000000
χ914-4-44-4-4444-4-44-44-244-4-4-4422-2-2-222-222-22-2-2-222-2200000000000000000000000000000000000000000000000000000000
χ924-4-44-4-444-44-444-4-24-44-44-422-2-2-2222-22-2-22-22-2-22200000000000000000000000000000000000000000000000000000000
χ9388-8-88i−8i8i−8i000000-4000000-444−4i4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ9488-8-8−8i8i−8i8i000000-4000000-4444i−4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ958-88-88i−8i−8i8i000000-40000004-444i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8−8i8i8i−8i000000-40000004-44−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.