Finite Group Databasebeta

← Group #10698599

Character table — Group #10698599

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444444444444444444444444444416161616161616161616161624242424242424242424242424242424
order122222223444444446666666448888888812121212121212121212121224242424242424242424242424242424444412121212121212122244444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1111111-1-1-1-1
χ9222222222222-2-2-22-22222222-2-200000000-2-2-2-2-2-22222-2-200000000000000000000000000002200-2-20000000000
χ10222222222222-2-2-22-22222222-2-200000000-2-2-2-2-2-22222-2-20000000000000000000000000000-2-200220000000000
χ11222222222-2-2-2222-222222222-2-2000000002222-2-2-2-2-2-2-2-20000000000000000000000000000002200-2-200000000
χ12222222222-2-2-2222-222222222-2-2000000002222-2-2-2-2-2-2-2-2000000000000000000000000000000-2-2002200000000
χ13222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-222-2-2-2-22200000000000000002-200000022-2-20000000000000000
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χ1522222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ1622222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ1722222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122-2-21111-1-1-1-10000000000000000
χ1822222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-222-1-1-1-111110000000000000000
χ1922222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122000000001111-1-11111-1-1−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i32-200−i3−i3i3i3-1-1110000000000000000
χ2022222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122000000001111-1-11111-1-1−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i3-2200i3i3−i3−i311-1-10000000000000000
χ2122222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122000000001111-1-11111-1-1i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i32-200i3i3−i3−i3-1-1110000000000000000
χ2222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122000000001111-1-11111-1-1i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3-2200−i3−i3i3i311-1-10000000000000000
χ23222-22-2-2-222-2-20002022-2-2-2-2200−i2−i2−i2−i2i2i2i2i200000022-2-200−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i200000000000000002i−2i0022−2−20000
χ24222-22-2-2-222-2-20002022-2-2-2-2200−i2−i2−i2−i2i2i2i2i200000022-2-200−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i20000000000000000−2i2i00−2−2220000
χ25222-22-2-2-222-2-20002022-2-2-2-2200i2i2i2i2−i2−i2−i2−i200000022-2-200i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i200000000000000002i−2i00−2−2220000
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χ2722-2-2-222-220002-2-2022-222-2-2-20022−2−222−2−222-2-20000000022−2−222−2−222−2−222−2−20000000000000000002i−2i0000−i2−i2i2i2
χ2822-2-2-222-220002-2-2022-222-2-2-20022−2−222−2−222-2-20000000022−2−222−2−222−2−222−2−2000000000000000000−2i2i0000i2i2−i2−i2
χ2922-2-2-222-220002-2-2022-222-2-2-200−2−222−2−22222-2-200000000−2−222−2−222−2−222−2−2220000000000000000002i−2i0000i2i2−i2−i2
χ3022-2-2-222-220002-2-2022-222-2-2-200−2−222−2−22222-2-200000000−2−222−2−222−2−222−2−222000000000000000000−2i2i0000−i2−i2i2i2
χ312-22-2-2-222200022-20-2-22-22-22-200−i2i2−i2i2−i2i2−i2i22-22-200000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000002i−2i000000002−22−2
χ322-22-2-2-222200022-20-2-22-22-22-200−i2i2−i2i2−i2i2−i2i22-22-200000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000000000−2i2i00000000−22−22
χ332-22-2-2-222200022-20-2-22-22-22-200i2−i2i2−i2i2−i2i2−i22-22-200000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000002i−2i00000000−22−22
χ342-22-2-2-222200022-20-2-22-22-22-200i2−i2i2−i2i2−i2i2−i22-22-200000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000000000−2i2i000000002−22−2
χ352-2-222-22-2222-22-22-2-2-2-2-222-22-22000000002-2-22-2-22-22-22200000000000000000000000000000000000000002i−2i−2i2i
χ362-2-222-22-2222-22-22-2-2-2-2-222-22-22000000002-2-22-2-22-22-2220000000000000000000000000000000000000000−2i2i2i−2i
χ372-2-222-22-2222-2-22-2-22-2-2-222-222-200000000-222-2222-22-2-2-20000000000000000002i−2i2i−2i2i−2i00000000000000000000
χ382-2-222-22-2222-2-22-2-22-2-2-222-222-200000000-222-2222-22-2-2-2000000000000000000−2i2i−2i2i−2i2i00000000000000000000
χ392-2-222-22-22-2-222-222-2-2-2-222-222-22i−2i−2i2i2i−2i−2i2i2-2-2222-22-22-2-22i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ402-2-222-22-22-2-222-222-2-2-2-222-222-2−2i2i2i−2i−2i2i2i−2i2-2-2222-22-22-2-2−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ412-2-222-22-22-2-22-22-222-2-2-222-22-2200000000-222-2-2-2-22-22220000000000000000000000000000000000002-22-20000
χ422-2-222-22-22-2-22-22-222-2-2-222-22-2200000000-222-2-2-2-22-2222000000000000000000000000000000000000-22-220000
χ432-2-222-22-2-122-2-22-2-22111-1-11-12-2000000001-1-11-1-1-11-11113−3−333−3−33−333−3−333−3002i−2i−ii−ii−i3i3−i3i30000000000000000
χ442-2-222-22-2-122-2-22-2-22111-1-11-12-2000000001-1-11-1-1-11-11113−3−333−3−33−333−3−333−300−2i2ii−ii−ii3−i3i3−i30000000000000000
χ452-2-222-22-2-122-2-22-2-22111-1-11-12-2000000001-1-11-1-1-11-1111−333−3−333−33−3−333−3−33002i−2i−ii−iii3−i3i3−i30000000000000000
χ462-2-222-22-2-122-2-22-2-22111-1-11-12-2000000001-1-11-1-1-11-1111−333−3−333−33−3−333−3−3300−2i2ii−ii−i−i3i3−i3i30000000000000000
χ472-2-222-22-2-1-2-222-222-2111-1-11-12-22i−2i−2i2i2i−2i−2i2i-111-1-1-11-11-111−iii−i−iii−i−iii−i−iii−i00003−3−33−i3i3i3−i30000000000000000
χ482-2-222-22-2-1-2-222-222-2111-1-11-12-22i−2i−2i2i2i−2i−2i2i-111-1-1-11-11-111−iii−i−iii−i−iii−i−iii−i0000−333−3i3−i3−i3i30000000000000000
χ492-2-222-22-2-1-2-222-222-2111-1-11-12-2−2i2i2i−2i−2i2i2i−2i-111-1-1-11-11-111i−i−iii−i−iii−i−iii−i−ii00003−3−33i3−i3−i3i30000000000000000
χ502-2-222-22-2-1-2-222-222-2111-1-11-12-2−2i2i2i−2i−2i2i2i−2i-111-1-1-11-11-111i−i−iii−i−iii−i−iii−i−ii0000−333−3−i3i3i3−i30000000000000000
χ512-2-2-222-222-22-200020-2-22-2-222002−2−22−222−2000000-222-2002−2−22−222−22−2−22−222−20000000000002-20000002−2−220000
χ522-2-2-222-222-22-200020-2-22-2-222002−2−22−222−2000000-222-2002−2−22−222−22−2−22−222−2000000000000-22000000−222−20000
χ532-2-2-222-222-22-200020-2-22-2-22200−222−22−2−22000000-222-200−222−22−2−22−222−22−2−220000000000002-2000000−222−20000
χ542-2-2-222-222-22-200020-2-22-2-22200−222−22−2−22000000-222-200−222−22−2−22−222−22−2−22000000000000-220000002−2−220000
χ5544444444-2444-4-4-44-4-2-2-2-2-2-2-2-4-400000000222222-2-2-2-22200000000000000000000000000000000000000000000
χ5644444444-2-4-4-4444-44-2-2-2-2-2-2-2-4-400000000-2-2-2-22222222200000000000000000000000000000000000000000000
χ57444-44-4-4-44-444000-4044-4-4-4-440000000000000000-4-4440000000000000000000000000000000000000000000000
χ58444-44-4-4-4-24-4-400040-2-22222-200−2i2−2i2−2i2−2i22i22i22i22i2000000-2-22200i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i20000000000000000000000000000
χ59444-44-4-4-4-24-4-400040-2-22222-2002i22i22i22i2−2i2−2i2−2i2−2i2000000-2-22200−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i20000000000000000000000000000
χ60444-44-4-4-4-2-444000-40-2-22222-2000000000000000022-2-2006666−6−6−6−6−6−6−6−666660000000000000000000000000000
χ61444-44-4-4-4-2-444000-40-2-22222-2000000000000000022-2-200−6−6−6−666666666−6−6−6−60000000000000000000000000000
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χ6344-44-4-4-444000000004-4-4-444-400−2i−2i2i2i2i2i−2i−2i000000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ6444-44-4-4-44-200000000-2222-2-22002i2i−2i−2i−2i−2i2i2i0000−2i32i30000−2i32i32ζ142ζ14−2ζ14−2ζ14−2ζ14−2ζ142ζ142ζ142ζ222ζ22−2ζ22−2ζ22−2ζ22−2ζ222ζ222ζ220000000000000000000000000000
χ6544-44-4-4-44-200000000-2222-2-22002i2i−2i−2i−2i−2i2i2i00002i3−2i300002i3−2i32ζ222ζ22−2ζ22−2ζ22−2ζ22−2ζ222ζ222ζ222ζ142ζ14−2ζ14−2ζ14−2ζ14−2ζ142ζ142ζ140000000000000000000000000000
χ6644-44-4-4-44-200000000-2222-2-2200−2i−2i2i2i2i2i−2i−2i0000−2i32i30000−2i32i3−2ζ14−2ζ142ζ142ζ142ζ142ζ14−2ζ14−2ζ14−2ζ22−2ζ222ζ222ζ222ζ222ζ22−2ζ22−2ζ220000000000000000000000000000
χ6744-44-4-4-44-200000000-2222-2-2200−2i−2i2i2i2i2i−2i−2i00002i3−2i300002i3−2i3−2ζ22−2ζ222ζ222ζ222ζ222ζ22−2ζ22−2ζ22−2ζ14−2ζ142ζ142ζ142ζ142ζ14−2ζ14−2ζ140000000000000000000000000000
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χ734-444-44-4-4400000000-444-44-4-4002-22-2-22-220000000000002-22-2-22-222-22-2-22-220000000000000000000000000000
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χ774-444-44-4-4-2000000002-2-22-22200-22-222-22-20000−2i32i300002i3−2i31−i3−1+i31−i3−1+i3−1+i31−i3−1+i31−i31+i3−1−i31+i3−1−i3−1−i31+i3−1−i31+i30000000000000000000000000000
χ784-444-44-4-4-2000000002-2-22-22200-22-222-22-200002i3−2i30000−2i32i31+i3−1−i31+i3−1−i3−1−i31+i3−1−i31+i31−i3−1+i31−i3−1+i3−1+i31−i3−1+i31−i30000000000000000000000000000
χ794-44-4-4-4444000-4-4404-44-44-44-40000000000-44-440000000000000000000000000000000000000000000000000000
χ804-44-4-4-444-200044-40-42-22-22-2200−2i22i2−2i22i2−2i22i2−2i22i2-22-2200000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000000000000000
χ814-44-4-4-444-200044-40-42-22-22-22002i2−2i22i2−2i22i2−2i22i2−2i2-22-2200000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000000000000000
χ824-44-4-4-444-2000-4-44042-22-22-2200000000002-22-2000000006−66−66−66−6−66−66−66−660000000000000000000000000000
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χ844-4-444-44-4-244-44-44-4-4222-2-22-2-4400000000-222-222-22-22-2-200000000000000000000000000000000000000000000
χ854-4-444-44-4-2-4-44-44-444222-2-22-2-44000000002-2-22222-22-2-2-200000000000000000000000000000000000000000000
χ864-4-4-444-4444-44000-40-4-44-4-44400000000000000004-4-440000000000000000000000000000000000000000000000
χ874-4-4-444-44-24-44000-4022-222-2-20000000000000000-222-200i6−i6−i6i6−i6i6i6−i6−i6i6i6−i6i6−i6−i6i60000000000000000000000000000
χ884-4-4-444-44-24-44000-4022-222-2-20000000000000000-222-200−i6i6i6−i6i6−i6−i6i6i6−i6−i6i6−i6i6i6−i60000000000000000000000000000
χ894-4-4-444-44-2-44-40004022-222-2-20022−22−2222−222222−220000002-2-2200−222−22−2−22−222−22−2−220000000000000000000000000000
χ904-4-4-444-44-2-44-40004022-222-2-200−222222−2222−22−22220000002-2-22002−2−22−222−22−2−22−222−20000000000000000000000000000

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