Finite Group Databasebeta

← Group #10698250

Character table — Group #10698250

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
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-1
χ711111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111
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
χ13222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-222-2-2-2-2220000000000000000002-222-2-200000000000000000000
χ14222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-222-2-2-2-222000000000000000000-22-2-22200000000000000000000
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−i3i3i3i3i3i3i3i3i3002-2-1-111−i3−i3i3i30000000000000000
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−i3i3i3i3i3i3i3i3i300-2211-1-1i3i3−i3−i30000000000000000
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−i3002-2-1-111i3i3−i3−i30000000000000000
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−i300-2211-1-1−i3−i3i3i30000000000000000
χ23222-2-22-2-2222-2000-2022-22-2-2-2002222−2−2−2−222-2-2000000002222−2−2−2−22222−2−2−2−20000000000002-200000022−2−20000
χ24222-2-22-2-2222-2000-2022-22-2-2-2002222−2−2−2−222-2-2000000002222−2−2−2−22222−2−2−2−2000000000000-22000000−2−2220000
χ25222-2-22-2-2222-2000-2022-22-2-2-200−2−2−2−2222222-2-200000000−2−2−2−22222−2−2−2−222220000000000002-2000000−2−2220000
χ26222-2-22-2-2222-2000-2022-22-2-2-200−2−2−2−2222222-2-200000000−2−2−2−22222−2−2−2−22222000000000000-2200000022−2−20000
χ2722-2-22-22-2200022-20-22-2-2-2-2220022−2−222−2−200000022-2-20022−2−222−2−222−2−222−2−20000000000000000002i−2i0000−i2−i2i2i2
χ2822-2-22-22-2200022-20-22-2-2-2-2220022−2−222−2−200000022-2-20022−2−222−2−222−2−222−2−2000000000000000000−2i2i0000i2i2−i2−i2
χ2922-2-22-22-2200022-20-22-2-2-2-22200−2−222−2−22200000022-2-200−2−222−2−222−2−222−2−2220000000000000000002i−2i0000i2i2−i2−i2
χ3022-2-22-22-2200022-20-22-2-2-2-22200−2−222−2−22200000022-2-200−2−222−2−222−2−222−2−222000000000000000000−2i2i0000−i2−i2i2i2
χ312-2222-2-2-222-222-22-2-2-2-2-222-222-2000000002-22-2222-22-2-2-200000000000000002-20000002-22-20000000000000000
χ322-2222-2-2-222-222-22-2-2-2-2-222-222-2000000002-22-2222-22-2-2-20000000000000000-22000000-22-220000000000000000
χ332-2222-2-2-222-22-22-2-22-2-2-222-22-22000000002-22-2-2-2-22-222200000000000000000000000000000000000000002i−2i2i−2i
χ342-2222-2-2-222-22-22-2-22-2-2-222-22-22000000002-22-2-2-2-22-22220000000000000000000000000000000000000000−2i2i−2i2i
χ352-2222-2-2-22-22-22-222-2-2-2-222-22-2200000000-22-22-2-22-22-2220000000000000000000000000000000000002i−2i2i−2i0000
χ362-2222-2-2-22-22-22-222-2-2-2-222-22-2200000000-22-22-2-22-22-222000000000000000000000000000000000000−2i2i−2i2i0000
χ372-2222-2-2-22-22-2-22-222-2-2-222-222-22i−2i2i−2i2i−2i2i−2i-22-2222-22-22-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ382-2222-2-2-22-22-2-22-222-2-2-222-222-2−2i2i−2i2i−2i2i−2i2i-22-2222-22-22-2-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ392-2222-2-2-2-12-222-22-2-2111-1-11-12-200000000-11-11-1-1-11-11113−33−33−33−3−33−33−33−332-2003−33−3-11-110000000000000000
χ402-2222-2-2-2-12-222-22-2-2111-1-11-12-200000000-11-11-1-1-11-11113−33−33−33−3−33−33−33−33-2200−33−331-11-10000000000000000
χ412-2222-2-2-2-12-222-22-2-2111-1-11-12-200000000-11-11-1-1-11-1111−33−33−33−333−33−33−33−32-200−33−33-11-110000000000000000
χ422-2222-2-2-2-12-222-22-2-2111-1-11-12-200000000-11-11-1-1-11-1111−33−33−33−333−33−33−33−3-22003−33−31-11-10000000000000000
χ432-2222-2-2-2-1-22-2-22-222111-1-11-12-22i−2i2i−2i2i−2i2i−2i1-11-1-1-11-11-111−ii−ii−ii−ii−ii−ii−ii−ii00003−3−33−i3i3i3−i30000000000000000
χ442-2222-2-2-2-1-22-2-22-222111-1-11-12-22i−2i2i−2i2i−2i2i−2i1-11-1-1-11-11-111−ii−ii−ii−ii−ii−ii−ii−ii0000−333−3i3−i3−i3i30000000000000000
χ452-2222-2-2-2-1-22-2-22-222111-1-11-12-2−2i2i−2i2i−2i2i−2i2i1-11-1-1-11-11-111i−ii−ii−ii−ii−ii−ii−ii−i00003−3−33i3−i3−i3i30000000000000000
χ462-2222-2-2-2-1-22-2-22-222111-1-11-12-2−2i2i−2i2i−2i2i−2i2i1-11-1-1-11-11-111i−ii−ii−ii−ii−ii−ii−ii−i0000−333−3−i3i3i3−i30000000000000000
χ472-22-2-2-2222-222000-20-2-222-22-200−i2i2−i2i2i2−i2i2−i2-222-200000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i200000000000000002-200−i2i2i2−i20000
χ482-22-2-2-2222-222000-20-2-222-22-200−i2i2−i2i2i2−i2i2−i2-222-200000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000-2200i2−i2−i2i20000
χ492-22-2-2-2222-222000-20-2-222-22-200i2−i2i2−i2−i2i2−i2i2-222-200000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i200000000000000002-200i2−i2−i2i20000
χ502-22-2-2-2222-222000-20-2-222-22-200i2−i2i2−i2−i2i2−i2i2-222-200000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000000000-2200−i2i2i2−i20000
χ512-2-2-222-222000-2220-2-222-2-2-2200−i2i2i2−i2−i2i2i2−i2000000-222-200−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000002i−2i000000002−2−22
χ522-2-2-222-222000-2220-2-222-2-2-2200−i2i2i2−i2−i2i2i2−i2000000-222-200−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i200000000000000−2i2i00000000−222−2
χ532-2-2-222-222000-2220-2-222-2-2-2200i2−i2−i2i2i2−i2−i2i2000000-222-200i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000002i−2i00000000−222−2
χ542-2-2-222-222000-2220-2-222-2-2-2200i2−i2−i2i2i2−i2−i2i2000000-222-200i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i200000000000000−2i2i000000002−2−22
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
χ57444-4-44-4-44-4-440004044-44-4-4-40000000000-4-4440000000000000000000000000000000000000000000000000000
χ58444-4-44-4-4-244-4000-40-2-22-22220022222222−22−22−22−22-2-22200000000−2−2−2−22222−2−2−2−222220000000000000000000000000000
χ59444-4-44-4-4-244-4000-40-2-22-222200−22−22−22−2222222222-2-222000000002222−2−2−2−22222−2−2−2−20000000000000000000000000000
χ60444-4-44-4-4-2-4-4400040-2-22-2222000000000022-2-200000000i6i6i6i6−i6−i6−i6−i6−i6−i6−i6−i6i6i6i6i60000000000000000000000000000
χ61444-4-44-4-4-2-4-4400040-2-22-2222000000000022-2-200000000−i6−i6−i6−i6i6i6i6i6i6i6i6i6−i6−i6−i6−i60000000000000000000000000000
χ6244-44-4-4-444000000004-44-44-4-40022-2-2-2-22200000000000022-2-2-2-22222-2-2-2-2220000000000000000000000000000
χ6344-44-4-4-444000000004-44-44-4-400-2-22222-2-2000000000000-2-22222-2-2-2-22222-2-20000000000000000000000000000
χ6444-44-4-4-44-200000000-22-22-2220022-2-2-2-2220000−2i32i30000−2i32i3−1−i3−1−i31+i31+i31+i31+i3−1−i3−1−i3−1+i3−1+i31−i31−i31−i31−i3−1+i3−1+i30000000000000000000000000000
χ6544-44-4-4-44-200000000-22-22-2220022-2-2-2-22200002i3−2i300002i3−2i3−1+i3−1+i31−i31−i31−i31−i3−1+i3−1+i3−1−i3−1−i31+i31+i31+i31+i3−1−i3−1−i30000000000000000000000000000
χ6644-44-4-4-44-200000000-22-22-22200-2-22222-2-20000−2i32i30000−2i32i31+i31+i3−1−i3−1−i3−1−i3−1−i31+i31+i31−i31−i3−1+i3−1+i3−1+i3−1+i31−i31−i30000000000000000000000000000
χ6744-44-4-4-44-200000000-22-22-22200-2-22222-2-200002i3−2i300002i3−2i31−i31−i3−1+i3−1+i3−1+i3−1+i31−i31−i31+i31+i3−1−i3−1−i3−1−i3−1−i31+i31+i30000000000000000000000000000
χ6844-4-44-44-44000-4-44044-4-4-4-4440000000000000000-4-4440000000000000000000000000000000000000000000000
χ6944-4-44-44-4-200044-40-4-22222-2-2002222−22−222222−22−22000000-2-22200−2−222−2−222−2−222−2−2220000000000000000000000000000
χ7044-4-44-44-4-200044-40-4-22222-2-200−22−222222−22−222222000000-2-2220022−2−222−2−222−2−222−2−20000000000000000000000000000
χ7144-4-44-44-4-2000-4-4404-22222-2-2000000000000000022-2-200i6i6−i6−i6i6i6−i6−i6−i6−i6i6i6−i6−i6i6i60000000000000000000000000000
χ7244-4-44-44-4-2000-4-4404-22222-2-2000000000000000022-2-200−i6−i6i6i6−i6−i6i6i6i6i6−i6−i6i6i6−i6−i60000000000000000000000000000
χ734-4444-4-4-4-24-44-44-4-44222-2-22-2-4400000000-22-22222-22-2-2-200000000000000000000000000000000000000000000
χ744-4444-4-4-4-2-44-44-444-4222-2-22-2-44000000002-22-222-22-22-2-200000000000000000000000000000000000000000000
χ754-44-4-4-44444-4-400040-4-444-44-400000000004-4-440000000000000000000000000000000000000000000000000000
χ764-44-4-4-444-24-4-40004022-2-22-220000000000-222-2000000006−66−6−66−66−66−666−66−60000000000000000000000000000
χ774-44-4-4-444-24-4-40004022-2-22-220000000000-222-200000000−66−666−66−66−66−6−66−660000000000000000000000000000
χ784-44-4-4-444-2-444000-4022-2-22-2200−2i22i2−2i22i22i2−2i22i2−2i22-2-2200000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000000000000000000000
χ794-44-4-4-444-2-444000-4022-2-22-22002i2−2i22i2−2i2−2i22i2−2i22i22-2-2200000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000000000000000
χ804-4-44-444-4400000000-44-4-444-4002i−2i−2i2i−2i2i2i−2i0000000000002i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ814-4-44-444-4400000000-44-4-444-400−2i2i2i−2i2i−2i−2i2i000000000000−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ824-4-44-444-4-2000000002-222-2-22002i−2i−2i2i−2i2i2i−2i0000−2i32i300002i3−2i32ζ22−2ζ22−2ζ222ζ22−2ζ222ζ222ζ22−2ζ222ζ14−2ζ14−2ζ142ζ14−2ζ142ζ142ζ14−2ζ140000000000000000000000000000
χ834-4-44-444-4-2000000002-222-2-22002i−2i−2i2i−2i2i2i−2i00002i3−2i30000−2i32i32ζ14−2ζ14−2ζ142ζ14−2ζ142ζ142ζ14−2ζ142ζ22−2ζ22−2ζ222ζ22−2ζ222ζ222ζ22−2ζ220000000000000000000000000000
χ844-4-44-444-4-2000000002-222-2-2200−2i2i2i−2i2i−2i−2i2i0000−2i32i300002i3−2i3−2ζ222ζ222ζ22−2ζ222ζ22−2ζ22−2ζ222ζ22−2ζ142ζ142ζ14−2ζ142ζ14−2ζ14−2ζ142ζ140000000000000000000000000000
χ854-4-44-444-4-2000000002-222-2-2200−2i2i2i−2i2i−2i−2i2i00002i3−2i30000−2i32i3−2ζ142ζ142ζ14−2ζ142ζ14−2ζ14−2ζ142ζ14−2ζ222ζ222ζ22−2ζ222ζ22−2ζ22−2ζ222ζ220000000000000000000000000000
χ864-4-4-444-4440004-4-404-444-4-4-4400000000000000004-4-440000000000000000000000000000000000000000000000
χ874-4-4-444-44-20004-4-4042-2-2222-20000000000000000-222-2006−6−666−6−66−666−6−666−60000000000000000000000000000
χ884-4-4-444-44-20004-4-4042-2-2222-20000000000000000-222-200−666−6−666−66−6−666−6−660000000000000000000000000000
χ894-4-4-444-44-2000-4440-42-2-2222-200−2i22i22i2−2i2−2i22i22i2−2i20000002-2-2200i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000000000000000000000000000
χ904-4-4-444-44-2000-4440-42-2-2222-2002i2−2i2−2i22i22i2−2i2−2i22i20000002-2-2200−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000000000000000000000000000

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