Finite Group Databasebeta

← Group #10698620

Character table — Group #10698620

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444444444444444444444444444416161616161616161616161624242424242424242424242424242424
order122222223444444446666666448888888812121212121212121212121224242424242424242424242424242424444412121212121212124444444488888888
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
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-1-1-1-1-11111
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-1
χ711111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ9222222222222-2-2-22-22222222-2-2000000002222-2-2-2-2-2-2-2-200000000000000000000000000002200-2-20000000000
χ10222222222222-2-2-22-22222222-2-2000000002222-2-2-2-2-2-2-2-20000000000000000000000000000-2-200220000000000
χ11222222222-2-2-2222-222222222-2-200000000-2-2-2-2-2-22222-2-20000000000000000000000000000002200-2-200000000
χ12222222222-2-2-2222-222222222-2-200000000-2-2-2-2-2-22222-2-2000000000000000000000000000000-2-2002200000000
χ13222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-222-2-2-2-2220000000000000000002-2000022-2-20000000000000000
χ14222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-222-2-2-2-222000000000000000000-220000-2-2220000000000000000
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
χ1722222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122-2-2-1-1-1-111110000000000000000
χ1822222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2221111-1-1-1-10000000000000000
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−i3i3i3i3i3i3i3i3i3002-2−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−i3i3i3i3i3i3i3i3i300-22i3i3−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−i3002-2i3i3−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−i300-22−i3−i3i3i311-1-10000000000000000
χ23222-2-2-2-2220002-2-20222-2-2-2-2200−i2−i2−i2−i2i2i2i2i200000022-2-200−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2000000000000002i−2i0000000022−2−2
χ24222-2-2-2-2220002-2-20222-2-2-2-2200−i2−i2−i2−i2i2i2i2i200000022-2-200−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i200000000000000−2i2i00000000−2−222
χ25222-2-2-2-2220002-2-20222-2-2-2-2200i2i2i2i2−i2−i2−i2−i200000022-2-200i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2000000000000002i−2i00000000−2−222
χ26222-2-2-2-2220002-2-20222-2-2-2-2200i2i2i2i2−i2−i2−i2−i200000022-2-200i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i200000000000000−2i2i0000000022−2−2
χ2722-222-2-2-2222-2000-202-222-2-2-20022−2−222−2−222-2-20000000022−2−222−2−222−2−222−2−20000000000002-200000022−2−20000
χ2822-222-2-2-2222-2000-202-222-2-2-20022−2−222−2−222-2-20000000022−2−222−2−222−2−222−2−2000000000000-22000000−2−2220000
χ2922-222-2-2-2222-2000-202-222-2-2-200−2−222−2−22222-2-200000000−2−222−2−222−2−222−2−2220000000000002-2000000−2−2220000
χ3022-222-2-2-2222-2000-202-222-2-2-200−2−222−2−22222-2-200000000−2−222−2−222−2−222−2−222000000000000-2200000022−2−20000
χ312-222-2-22-222-2-200020-22-22-22-200−i2i2−i2i2−i2i2−i2i22-22-200000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000000000002-200−i2i2−i2i20000
χ322-222-2-22-222-2-200020-22-22-22-200−i2i2−i2i2−i2i2−i2i22-22-200000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000-2200i2−i2i2−i20000
χ332-222-2-22-222-2-200020-22-22-22-200i2−i2i2−i2i2−i2i2−i22-22-200000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000000000002-200i2−i2i2−i20000
χ342-222-2-22-222-2-200020-22-22-22-200i2−i2i2−i2i2−i2i2−i22-22-200000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000-2200−i2i2−i2i20000
χ352-2-22-22-2222-2222-2-2-2-2-2-222-22-22000000002-2-22-2-22-22-2220000000000000000000000000000000000002i−2i−2i2i0000
χ362-2-22-22-2222-2222-2-2-2-2-2-222-22-22000000002-2-22-2-22-22-222000000000000000000000000000000000000−2i2i2i−2i0000
χ372-2-22-22-2222-22-2-22-22-2-2-222-222-22i−2i−2i2i2i−2i−2i2i2-2-2222-22-22-2-22i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ382-2-22-22-2222-22-2-22-22-2-2-222-222-2−2i2i2i−2i−2i2i2i−2i2-2-2222-22-22-2-2−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ392-2-22-22-222-22-222-22-2-2-2-222-222-200000000-222-2222-22-2-2-200000000000000002i−2i002i−2i2i−2i00000000000000000000
χ402-2-22-22-222-22-222-22-2-2-2-222-222-200000000-222-2222-22-2-2-20000000000000000−2i2i00−2i2i−2i2i00000000000000000000
χ412-2-22-22-222-22-2-2-2222-2-2-222-22-2200000000-222-2-2-2-22-222200000000000000000000000000000000000000002-22-2
χ422-2-22-22-222-22-2-2-2222-2-2-222-22-2200000000-222-2-2-2-22-22220000000000000000000000000000000000000000-22-22
χ432-2-22-22-22-12-22-2-22-22111-1-11-12-22i−2i−2i2i2i−2i−2i2i-111-1-1-11-11-111−iii−i−iii−i−iii−i−iii−i00003−3−33−i3i3−i3i30000000000000000
χ442-2-22-22-22-12-22-2-22-22111-1-11-12-22i−2i−2i2i2i−2i−2i2i-111-1-1-11-11-111−iii−i−iii−i−iii−i−iii−i0000−333−3i3−i3i3−i30000000000000000
χ452-2-22-22-22-12-22-2-22-22111-1-11-12-2−2i2i2i−2i−2i2i2i−2i-111-1-1-11-11-111i−i−iii−i−iii−i−iii−i−ii00003−3−33i3−i3i3−i30000000000000000
χ462-2-22-22-22-12-22-2-22-22111-1-11-12-2−2i2i2i−2i−2i2i2i−2i-111-1-1-11-11-111i−i−iii−i−iii−i−iii−i−ii0000−333−3−i3i3−i3i30000000000000000
χ472-2-22-22-22-1-22-222-22-2111-1-11-12-2000000001-1-11-1-1-11-11113−3−333−3−33−333−3−333−32i−2i00−ii−ii−i3i3i3−i30000000000000000
χ482-2-22-22-22-1-22-222-22-2111-1-11-12-2000000001-1-11-1-1-11-11113−3−333−3−33−333−3−333−3−2i2i00i−ii−ii3−i3−i3i30000000000000000
χ492-2-22-22-22-1-22-222-22-2111-1-11-12-2000000001-1-11-1-1-11-1111−333−3−333−33−3−333−3−332i−2i00−ii−iii3−i3−i3i30000000000000000
χ502-2-22-22-22-1-22-222-22-2111-1-11-12-2000000001-1-11-1-1-11-1111−333−3−333−33−3−333−3−33−2i2i00i−ii−i−i3i3i3−i30000000000000000
χ512-2-2-22-2222000-22-202-2-22-2-222002−2−22−222−2000000-222-2002−2−22−222−22−2−22−222−20000000000000000002-200002−2−22
χ522-2-2-22-2222000-22-202-2-22-2-222002−2−22−222−2000000-222-2002−2−22−222−22−2−22−222−2000000000000000000-220000−222−2
χ532-2-2-22-2222000-22-202-2-22-2-22200−222−22−2−22000000-222-200−222−22−2−22−222−22−2−220000000000000000002-20000−222−2
χ542-2-2-22-2222000-22-202-2-22-2-22200−222−22−2−22000000-222-200−222−22−2−22−222−22−2−22000000000000000000-2200002−2−22
χ5544444444-2444-4-4-44-4-2-2-2-2-2-2-2-4-400000000-2-2-2-22222222200000000000000000000000000000000000000000000
χ5644444444-2-4-4-4444-44-2-2-2-2-2-2-2-4-400000000222222-2-2-2-22200000000000000000000000000000000000000000000
χ57444-4-4-4-444000-4440-444-4-4-4-440000000000000000-4-4440000000000000000000000000000000000000000000000
χ58444-4-4-4-44-20004-4-404-2-22222-200−2i2−2i2−2i2−2i22i22i22i22i2000000-2-22200i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i20000000000000000000000000000
χ59444-4-4-4-44-20004-4-404-2-22222-2002i22i22i22i2−2i2−2i2−2i2−2i2000000-2-22200−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i20000000000000000000000000000
χ60444-4-4-4-44-2000-4440-4-2-22222-2000000000000000022-2-2006666−6−6−6−6−6−6−6−666660000000000000000000000000000
χ61444-4-4-4-44-2000-4440-4-2-22222-2000000000000000022-2-200−6−6−6−666666666−6−6−6−60000000000000000000000000000
χ6244-444-4-4-44-4-44000404-444-4-4-40000000000-4-4440000000000000000000000000000000000000000000000000000
χ6344-444-4-4-4-244-4000-40-22-2-2222002222−22−222222−22−22-2-22200000000−2−222−2−222−2−222−2−2220000000000000000000000000000
χ6444-444-4-4-4-244-4000-40-22-2-222200−22−222222−22−222222-2-2220000000022−2−222−2−222−2−222−2−20000000000000000000000000000
χ6544-444-4-4-4-2-4-4400040-22-2-2222000000000022-2-200000000i6i6−i6−i6i6i6−i6−i6−i6−i6i6i6−i6−i6i6i60000000000000000000000000000
χ6644-444-4-4-4-2-4-4400040-22-2-2222000000000022-2-200000000−i6−i6i6i6−i6−i6i6i6i6i6−i6−i6i6i6−i6−i60000000000000000000000000000
χ6744-4-4-444-44000000004-4-4-444-4002i2i−2i−2i−2i−2i2i2i0000000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ6844-4-4-444-44000000004-4-4-444-400−2i−2i2i2i2i2i−2i−2i000000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ6944-4-4-444-4-200000000-2222-2-22002i2i−2i−2i−2i−2i2i2i0000−2i32i30000−2i32i32ζ142ζ14−2ζ14−2ζ14−2ζ14−2ζ142ζ142ζ142ζ222ζ22−2ζ22−2ζ22−2ζ22−2ζ222ζ222ζ220000000000000000000000000000
χ7044-4-4-444-4-200000000-2222-2-22002i2i−2i−2i−2i−2i2i2i00002i3−2i300002i3−2i32ζ222ζ22−2ζ22−2ζ22−2ζ22−2ζ222ζ222ζ222ζ142ζ14−2ζ14−2ζ14−2ζ14−2ζ142ζ142ζ140000000000000000000000000000
χ7144-4-4-444-4-200000000-2222-2-2200−2i−2i2i2i2i2i−2i−2i0000−2i32i30000−2i32i3−2ζ14−2ζ142ζ142ζ142ζ142ζ14−2ζ14−2ζ14−2ζ22−2ζ222ζ222ζ222ζ222ζ22−2ζ22−2ζ220000000000000000000000000000
χ7244-4-4-444-4-200000000-2222-2-2200−2i−2i2i2i2i2i−2i−2i00002i3−2i300002i3−2i3−2ζ22−2ζ222ζ222ζ222ζ222ζ22−2ζ22−2ζ22−2ζ14−2ζ142ζ142ζ142ζ142ζ14−2ζ14−2ζ140000000000000000000000000000
χ734-444-4-44-44-444000-40-44-44-44-40000000000-44-440000000000000000000000000000000000000000000000000000
χ744-444-4-44-4-24-4-4000402-22-22-2200−2i22i2−2i22i2−2i22i2−2i22i2-22-2200000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000000000000000
χ754-444-4-44-4-24-4-4000402-22-22-22002i2−2i22i2−2i22i2−2i22i2−2i2-22-2200000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000000000000000
χ764-444-4-44-4-2-444000-402-22-22-2200000000002-22-2000000006−66−66−66−6−66−66−66−660000000000000000000000000000
χ774-444-4-44-4-2-444000-402-22-22-2200000000002-22-200000000−66−66−66−666−66−66−66−60000000000000000000000000000
χ784-44-444-4-4400000000-444-44-4-4002-22-2-22-220000000000002-22-2-22-222-22-2-22-220000000000000000000000000000
χ794-44-444-4-4400000000-444-44-4-400-22-222-22-2000000000000-22-222-22-2-22-222-22-20000000000000000000000000000
χ804-44-444-4-4-2000000002-2-22-222002-22-2-22-220000−2i32i300002i3−2i3−1+i31−i3−1+i31−i31−i3−1+i31−i3−1+i3−1−i31+i3−1−i31+i31+i3−1−i31+i3−1−i30000000000000000000000000000
χ814-44-444-4-4-2000000002-2-22-222002-22-2-22-2200002i3−2i30000−2i32i3−1−i31+i3−1−i31+i31+i3−1−i31+i3−1−i3−1+i31−i3−1+i31−i31−i3−1+i31−i3−1+i30000000000000000000000000000
χ824-44-444-4-4-2000000002-2-22-22200-22-222-22-20000−2i32i300002i3−2i31−i3−1+i31−i3−1+i3−1+i31−i3−1+i31−i31+i3−1−i31+i3−1−i3−1−i31+i3−1−i31+i30000000000000000000000000000
χ834-44-444-4-4-2000000002-2-22-22200-22-222-22-200002i3−2i30000−2i32i31+i3−1−i31+i3−1−i3−1−i31+i3−1−i31+i31−i3−1+i31−i3−1+i3−1+i31−i3−1+i31−i30000000000000000000000000000
χ844-4-44-44-44-24-4444-4-4-4222-2-22-2-4400000000-222-222-22-22-2-200000000000000000000000000000000000000000000
χ854-4-44-44-44-2-44-4-4-4444222-2-22-2-44000000002-2-22222-22-2-2-200000000000000000000000000000000000000000000
χ864-4-4-44-44440004-440-4-4-44-4-44400000000000000004-4-440000000000000000000000000000000000000000000000
χ874-4-4-44-444-20004-440-422-222-2-20000000000000000-222-200i6−i6−i6i6−i6i6i6−i6−i6i6i6−i6i6−i6−i6i60000000000000000000000000000
χ884-4-4-44-444-20004-440-422-222-2-20000000000000000-222-200−i6i6i6−i6i6−i6−i6i6i6−i6−i6i6−i6i6i6−i60000000000000000000000000000
χ894-4-4-44-444-2000-44-40422-222-2-20022−22−2222−222222−220000002-2-2200−222−22−2−22−222−22−2−220000000000000000000000000000
χ904-4-4-44-444-2000-44-40422-222-2-200−222222−2222−22−22220000002-2-22002−2−22−222−22−2−22−222−20000000000000000000000000000

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